Phil Foden's 82nd-minute goal was shortly followed by the ball striking the arm of midfielder Rodri. Referee Paul Tierney had not given a decision on the pitch and VAR official Kavanagh ruled there was no reason to change that.

The fury of the home fans was matched by that of coach Ashley Cole, who was shown a yellow card for his protestations to Tierney after the final whistle.

"There is no doubt, there is no probably to it," said Lampard on whether his side should have been awarded a spot-kick.

"The decision is incredible, incredible, and that loses us the opportunity to get what we deserved.

"That's a VAR call. That's Chris Kavanagh, I spoke to the referee and they know it is a penalty, the question is that is it offside and it wasn't. That's the reason we have VAR. It wouldn't have needed more than five seconds to know it was a penalty. He [Kavanagh] should have either told the referee to give it or told him to go look at it.

"We've lost a point because of a professional who cannot do his job right. You start searching for whys and I can't think why. It is so incompetent to get it wrong.

"Pep will know, Everton fans will know, Man City fans will know, it was the clearest penalty you could give: arm is out - great, below the sleeve - great, I was waiting for the penalty.

"Incompetence at best, at worst who knows? I'll wait for the statement or apology they do when things are wrong but it will mean nothing."

• Everton 0-1 Man City - Match report and highlights
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'My three-year old daughter could tell you that was a penalty'

Lampard's comments will almost inevitably attract the attention of the Football Association, who take a dim view of managers criticising the integrity of officials, but the Everton boss was clearly frustrated at a decision that could prove crucial in Everton's bid to beat relegation.

"I was calm, I was not shouting and ranting at him," Lampard added to Sky Sports. "I wanted to know if offside in the build up but I have been told it wasn't in the build up.

"Go to VAR, they have two minutes to look at it and to think they have not given that as a penalty when it strikes him on the arm, in an unnatural position. I have a three-year-old daughter at home who could tell you that was a penalty.

"We are fighting at the bottom of the table and they are fighting at the top. Decisions are crucial. I don't know what has to happen as a reflection of that. A mistake is when you have done something wrong and don't have time to think about it, they had two minutes to digest the handball.

"Even if the VAR says not sure, then go have a look. It is incompetence at best, if not that then someone needs to explain what it is."

'It was offside' | Pep Guardiola shuts down handball talk

Meanwhile, Pep Guardiola had a different view, saying he had not seen replays of the incident but believed the right decision had been made.

Asked about the controversial decision to deny Everton a penalty for an apparent handball, Guardiola said: "It was offside. There was VAR and the action was offside. I didn't see the image."

He added: "When VAR reviews things anything can happen but I think the referee gave offside for the pass from Dele Ali to Richarlison, that is what I figured out in that moment.

'My heart was in my mouth' | What the players said

Everton midfielder Alex Iwobi: "My friends have shown me and we all think its a penalty. We can't do anything about it now.

"When I was coming off at the end, Ashley Cole was saying 'it was a pen' and surprised the referee didn't have a choice to see it.

"We think it was clear cut. The decision has been made, we have to get on with it."

Manchester City forward Phil Foden: "I was just praying, fingers crossed it was not a penalty. I didn't get a good sight of it but my heart was in my mouth."

Manchester City defender John Stones: "I didn't get a good view of it when it happened. The ball went out and VAR checked and you are just waiting then."

'How is that not clear?' | What did the pundits say?

Former Man City defender and Sky Sports pundit Micah Richards:

"Rodri's face said it all. It's handball. It is below the T-shirt line.

"It's just ridiculous. We've talked about VAR so many times and they have got so many things right, but this one they have got wrong, and it has cost Everton dearly.

"It's costing everyone involved in the Premier League. Forget Liverpool for a minute and what they are doing, Everton need to stay up. If they get a penalty and potentially a point out of the game, it enhances their chances.

"How can that not be clear enough evidence? We've just got to tell the truth and it is handball. Chris Kavanagh has got one wrong."

Sky Sports' Karen Carney:

"For me, it was a penalty. The ball then bounces up and there's back spin on it. Rodri puts out his arm and the ball hits it.

"Obviously, there is the T-shirt line rule, which means if it hits on the T-shirt it is not handball, but for me it is. I can't believe they didn't say to the referee go over to the screen and have a look.

"I can understand why the Everton and the Everton fans are aggrieved."

Sky Sports' Andy Hincliffe:

"We'd have to see whether Paul Tierney actually saw Rodri's arm and saw the ball. If he hasn't seen it, of course, VAR is there. They are constantly assessing the game. That is their job to then step in, asses that situation and then either make a decision or throw it back to the referee to go and have a look at the monitor.

"It looked pretty obvious to me that it was a handball. There's spin on the ball, Rodri's arm comes out and it seems to clearly strike his arm.

"I am a fan of VAR but on this occasion I don't understand them saying there is not enough evidence to see that the ball hit his arm. We've just seen the pictures again and it is obvious. You can also see how guilty Rodri looks. He knows his arm has come out and the ball has struck it.

"VAR took their time, there was no rushed decision and I thought clearly they were looking at this and they are going to give a handball. It was a handball and they don't even refer it back down to the referee.

Hinchcliffe added: "The referee is kind of looking through the body of Rodri. He hasn't got the best view, but he should be relying on his assistants and VAR."

"That is what VAR is there for, situations like this where the referee has to think if he's seen it and can he see it. If they can't see it, VAR steps in and here, they should have done their job."

"They feel they have but we all think it was a handball and Rodri and City have got away with one."