Antonio Rudiger scored the only goal of the second leg at Tottenham Hotspur Stadium on Wednesday as the European champions secured a 3-0 aggregate win over their London rivals.
It was a frustrating night for Spurs, who were awarded a penalty in each half by Andre Marriner, but the decisions were both correctly overturned.
Marriner pointed the spot in the first half for a foul by Rudiger on Pierre-Emile Hojbjerg, but the VAR informed the referee that contact was made outside the box.
The referee then realised he got it wrong again when he took a look on the pitchside monitor after ruling that Lucas Moura had been upended by Kepa Arrizabalaga, who clearly got the ball when he came out to deny the Spurs forward.
Harry Kane then had a goal disallowed for offside following another VAR check and Chelsea saw out another victory to set up a final against Arsenal or Liverpool on February 27.
Yet Blues boss Tuchel was not impressed with the way his side went about booking another trip to Wembley.
The German told Sky Sports: "I think we started okay, started good. We created big chances, we were in the lead, but we played with fire.
"We allowed chances from easy and sloppy mistakes and we were lucky, almost gave a penalty away for absolutely no reason, from a bit of over-confidence.
"We started again very well in the second half and the same happened for the last 20-25 minutes. There was a mixture of lack of focus, over-confidence, I don't know. Suddenly we need luck to not have another penalty [awarded against them], to have another VAR decision with a little offside.
"We can play much better, we need to play much better if we want to really deserve results like this because we did play well over long phases of the match, but we need to do better."
Asked if he was unhappy with the performance, he replied: "Yes, we need to have the standards because that is why we work for Chelsea and we play for Chelsea and nothing else matters.
"It's about our standards and not about getting a result somehow. We can do much better, we can close spaces much better, we can do better defending individually, we can control the match better with less mistakes.
"In any part of the match we can do better and we have to do better."