The Blues are firmly in the race for a top four spot, after securing fourth position in the league table with a 2-0 win over Newcastle United.
They have now won four games in a row under Tuchel, and have 13 points from 15 since he took over.
But the German is not getting carried away, and would prefer the Blue take it one game at a time.
He told reporters after beating Newcastle: “We will never stop pushing because like I said before, there is no other way than taking it step by step and game by game.
“I can only tell everybody there is a long way to go, there are many many teams who are close and we have some tough games, a lot of big teams to play and points to win.
“Many people said when we started that [top four] wouldn’t be possible because there were many places and points between us and Liverpool in fourth place. It was clear that it was not all in our hands and we needed results on other pitches to close the gap. This was the situation when we started. From then on, we spent not one minute thinking about the other pitches and other teams, the situations with the fixtures.
“We just spent every minute with our team focusing on us. To prepare for matches because we play in the toughest league and we need to be ready every three days.”
Tuchel added: “The only focus will be on how to be ready for Southampton. I think that my players know this very well. We worked hard for this momentum. The players have worked incredibly hard to win all these games in a row and it will not stop. That’s the bad news, but everybody is prepared for that.
“Everybody who signs for Chelsea wants to have this competition and the challenge is now to keep on going. But we can look at our performance, determination and hunger to not allow anybody to drop to 99% performance levels.”