James whipped a corner into the Liverpool box on 22 minutes which Havertz flicked into the net for the match's opening goal.
However, Chelsea were left on the back foot three minutes into added time at the end of the first half when James handled the ball on the line after a Sadio Mane shot.
Referee Anthony Taylor consulted VAR and the 21-year-old was sent off for preventing a goal chance with his arm.
"The red card -- I'm not even sure any more if it's the rules or not the rules. You have to accept the decision. He maybe would have changed his mind with moving pictures," Tuchel said after the match.
"In the end it maybe would have stayed the same. I don't like early red cards in general because it spoils the game. In the end it was a tough and hard fight. We showed great resilience and deserved the point.
"We decided to stay in a back five. We wanted to stay active and make it hard to create chances. The first 10 minutes seemed endless. The last five minutes I was actually praying we take what we deserved. It was a hard and a tough one, but a very strong second half defensively."
Liverpool manager Jurgen Klopp also wasn't sure that James deserved to be sent off for the incident.
"I never liked double punishment but if somebody ever listened to me about rule changes or rules, a lot of things would look completely different," Klopp said.
"It was absolutely harsh. Spoils the game? Yeah probably. It changed everything, I liked our first half, we were really good, caused Chelsea a lot of problems. It was an incredible intense game from Chelsea as well.
"I would have loved to have seen the game in an 11 vs. 11 situation and see who comes through better but it's the way it is."
Liverpool dominated possession in the second half but couldn't find a winning goal.
"Everything was enjoyable apart from the result. I saw two very good football teams. It was a great first half from us and actually a good second one because it's so tricky when you play against nine defenders and have to create and create," Klopp said.
"Second half everyone thinks 'come on.' There is a definite advantage in possession, you have to out-number them and defend them really high, but the defensive structure changes in that case that they are only defending slightly deeper but they have eight players defending that area around the box so we couldn't use that.
"We had our shots from distance, I would have loved to have been a bit closer for the rebound but it was a good game."