Chelsea boss Thomas Tuchel, speaking to Match of the Day, said: "We had the better chances and played high up the pitch in the second half. We have to accept a draw in the end and a clean sheet. We had a very good reaction after half time. We stepped up and got better and better with higher recoveries. We went for a win but it did not happen.
"In this highest level, at some points, maybe two big chances have to be enough. If you don't do that then we have to be alert and aware of the counter-attacks and quality from Manchester United. We did this and defended very well. This was extraordinary effort and quality. We take it and go on."
On the VAR no-penalty decision, Tuchel added: "I was anxious before I thought I was totally wrong. From my point of view it was totally clear that a man in red touched it. When I saw it on the iPad I could not understand what was going on as it was only the man with the red shirt who touched it. I did not understand what the check was for.
Manchester United manager Ole Gunnar Solskjaer, speaking to Match of the Day, said: "It was a penalty, 100% nailed on. If that's a natural position for a hand to be in when the ball comes in then I must be blind.
"We wanted to win. Apart from the last quality or pass being not good enough, we had great pressing, desire [and] work-rate. There was a great save by David de Gea and we got the clean sheet.
"That's what let us down, that quality on the ball. The first half was scrappy. Poor game really. But then we played some good stuff at times. When we settled we created a few chances but we didn't have enough.