Rather than gaining points in those games, it has more often been a case of dropping two, which is why Tuchel now wants to see his side fully rewarded for their efforts.
"We need to be more effective," he said. "We need to be more ruthless than we have been in our recent games."
Tuchel insists his side's form is not a concern, though, and they remain just two points adrift of the top six and a place in Europe for next season.
"The four draws have not put us under any particular pressure," Tuchel told reporters.
"It's not the case that we are lacking any fundamentals. It is more the case that we are putting a lot into the games but not getting enough out of them.
"That can only lead us to wanting to turn things around against Leverkusen, but that's going to be tough."
Indeed, Mainz come up against the third-strongest side in Germany, considering the current league table, and they are keen to maintain that position to secure Champions League football.
And they have been given a boost with the news that captain Simon Rolfes has extended his contract by two years.
"I'm delighted by that," said joint-coach Sami Hyypia. "He is our captain and a very good and important player, also in the dressing room.
"Simon always has a positive influence on things."
Rolfes is set to make his 224th appearance for the club tomorrow, and many more are now set to follow.
"I have had a wonderful and successful time with Bayer and we want to develop step by step," the 31-year-old told his club's official website.
"We have the right blend of experienced and young, talented players and I want to make my contribution to us being successful in the future."