The main talking point of the first half came on 15 minutes when United were refused a penalty by referee Stuart Attwell.
The ball bounced off Callum Hudson-Odoi's hand as he tussled with Mason Greenwood in the box but, after a VAR review, Attwell found that Hudson-Odoi didn't move his arm towards the ball and thus it wasn't a penalty offence.
Tuchel was adamant after the game that it wasn't a penalty or even necessary of a VAR review.
"How can this be a VAR intervention? The player in red plays the ball with the hand and then we are checking for a penalty? Why does the referee have to see this," he said.
"I've seen it on the iPad, I don't understand why the referee has to check it but I'm glad it was no penalty. That would make it even worse."
However, his United counterpart Ole Gunnar Soskjaer was less than happy with Attwell's decision.
"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," he said after the game.
Hakim Ziyech had a great opportunity to open the scoring for Chelsea three minutes into the second half when Ben Chilwell struck a cross into the box. However, rather than putting the ball into the empty space on David de Gea's right, Ziyech struck the ball straight at the United No. 1.
Despite Chelsea enjoying the majority of the possession -- they had over 80% for the first 10 minutes of the second half -- United had their chances too with the best falling to Scott McTominay on the hour mark.
United played the ball around the box before eventually it found its way to McTominay on the right who struck a strong ball at Edouard Mendy who did enough to save it.
"I thought we were closer to winning it, but there was a lot of quality on the pitch," Tuchel added. "Performance-wise I'm satisfied. We defended very well in the last line and I'm very happy with that.
"We take what we got. I'm absolutely happy. Against a team like Man United you don't get many chances."