The Blues remain unbeaten under the German coach but lacked the quality to carve open Ole Gunnar Solskjaer’s men.
Chelsea survived an early scare when Callum Hudson-Odoi appeared to have handled the ball inside his own area during the opening stages of the game.
Referee Stuart Attwell denied a potential penalty after a long view from the pitch side monitor.
"It was a high-quality game between two very strong teams,” Tuchel told Sky Sports after the game.
“We suffered in some minutes in the first half, because of the quality of McTominay. Overall, it was an even game. We felt very strong second half, good chances, good half-chances, I thought we were closer to win it, but there was a lot of quality on the pitch, anything can happen. I'm satisfied, we defended very high, very encouraged.
"We changed in the second half and defended with two strikers to block them so they cannot come forward with the ball - and we were not good enough attacking the space, they started pressing high so to find the solution was not always easy. We lost confidence with a lot of easy ball losses.
"We're not in that moment where we are clinical enough to win games like this. But with the effort and performance, absolutely no concerns. If we go on like this, we are a difficult team to play against."
Next up for Chelsea is a daunting trip to Anfield to face Jurgen Klopp’s Liverpool in the Premier League on Thursday.
