However, a loss to Leicester City at Wembley on Saturday has seen the first attempt at silverware come and go, while a home loss to Arsenal - combined with wins for Liverpool - means the Blues only hold a one-point advantage over the Reds in the race for the top four with two games remaining.
Chelsea have the chance to gain a measure of revenge against third-placed Leicester when they meet in the league on Tuesday. A win will move Tuchel's side above the Foxes, but a draw or defeat will open the door for Liverpool, who play Burnley on Wednesday, to replace them in fourth.
Chelsea then face Aston Villa in their final game of the season on Sunday before taking on league champions Manchester City in the Champions League final on May 29.
With the pressure on, Tuchel has said he has full faith in his players and has urged them to embrace the challenge.
"This is a strong group," Tuchel told the Chelsea website. "There is no reason to doubt these players, who have done so well to get into the top four from 10th place, to reach the FA Cup final and to be in the final of the Champions League.
"We are strong enough to handle these situations and these are the challenges that we face.
"It's not easy, but it is fun, and there are a lot of teams chasing us and our situation."
Chelsea v Leicester: FA Cup final ratings
Central to Chelsea's resurgence, and to their hopes of a strong finish to the season, is midfielder Mason Mount.
The England international has been in fine form this season and was denied an equaliser in the FA Cup final by a spectacular save from Leicester keeper Kasper Schmeichel.
Tuchel reiterated Mount's importance to his team and expects him to play a major role in the final few games.
"We tried to give Mason a little break recently because he gave a lot in the Real Madrid games and he has been so decisive for us," Tuchel said.
"In the cup final, perhaps he could have played with a little more composure but don’t forget, if it wasn’t for an incredible save from Schmeichel, then he would have scored an equaliser.
"It wasn’t to be but Mason is always a dangerous player for us and we should be careful that we don’t over-expect from Mason.
"He is a key player for us in every match, he’s always so decisive and that will not change for the next three matches. He is absolutely key for us."