Havertz was involved in both goals, seeing his deflected effort beat Jordan Pickford in the first half and then winning a penalty for Jorginho to convert after the break.
It was the £71million man’s best display in a Chelsea shirt since he contracted Covid-19 in November.
Tuchel said: “I am very happy with his performance. There is no doubt about his quality, talent and character.
“He needs to adapt to the Premier League and to the club where we play to win every game and the highest standards are normal.
“This kind of mentality, but I think he did it today excellently, he got in good positions and used his potential to accelerate our game and to increase the touches in the box responsible for assists, to take responsibility to finish himself. This is what we want from him.”
An 11th straight game without defeat since Tuchel took charge has put Chelsea on course for Champions League qualification.
The German is convinced they have the quality to finish in the top four.
He added: “I truly believe that this sport is about team effort, I can feel the strong bond between the players, they are not talking about it, but they live it in training and this is what you see on the pitch.
“I can feel it on the side line, I can feel the support and I feel the positive energy from everybody around the team towards my staff.
Everybody is doing everything in a really positive atmosphere and we need this to continue.”