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Chelsea captain Cesar Azpilicuetafelt the Blues deserved a penalty for an incident involving himself and Harry Maguire, adding that he thought the referee should have reviewed the decision.
Former United star Patrice Evra likened Maguire to Hulk Hogan after the incident, saying that the WWE-like manoeuvrewas a clear penalty.
The referee, disagreed, opting to let play continue on in what ended up being a 0-0 draw.
After the match, Azpilicueta acknowledged that it was a difficult call in real-time, but said that VAR should have been able to clear up any uncertainty.
"A good question, on the pitch I felt yes and I felt arms around my neck and shoulders," he told Sky Sports.
"The referee can make the decision, the VAR is there to help. In any situation, the referee takes the main decisions and the monitor is there for him to help.
"It was 50-50 so why not take 20 seconds to review it? I think VAR can improve a lot. It happens, it is football, I don't say every time there is contact there should be a penalty.
"In England, there is strong physical contact. In football and in the Premier League always we should seek improvement - it is not a criticism, we can all help together to make a better league."
Chelsea's high-powered, big-money attack was largely held quiet on Saturday, with the Blues playing a more cautious game against United at Old Trafford.
United, meanwhile, tested Chelsea's Edouard Mendy several times, with the new starting goalkeeper making a fantastic save late on to keep out a potential Marcus Rashford winner.
The match was one that left Chelsea wanting more, Azpilicueta says, as the Blues did not play at a level anywhere near their best in his opinion.
"I have the feeling we could have done more. We found spaces but we didn't create the last pass or pick the right pass or make the right decisions," he said.
"We defended solid and they have at the end one save by Edouardand in the first half one mistake by us, but we could do more.
"For moments we had spells. In the first half we controlled better but in the second half sometimes we rushed it and didn't move the ball good enough.
"We lost possession too easily which meant we lost some control but we showed solidity and it was a great effort from everybody. Obviously, we want more."
He added: "We have a long season to go and hopefully we can keep improving. We have the quality to do it."