The reigning champions are in top spot on 59 points, two ahead of Borussia Dortmund with six games left, but they have gone through some turbulent weeks that saw them crash out of the German Cup and Champions League in 14 days.
In the Cup, it was Freiburg who beat them in Munich while City advanced with a comfortable 4-1 aggregate win after Wednesday's match.
Tuchel, who previously coached Chelsea and Paris St Germain, was brought in following the surprise sacking of Julian Nagelsmann in late March.
Club bosses had said the season goals were at risk and they had to act but just over three weeks later all Bayern have left to fight for is the domestic league crown.
"At the end of the day, we are just scoring far too few goals," said midfielder Thomas Muller. "The effort we put in is brutal but we are missing the coolness and that punch.
"We just don't put the ball in but narrowly wide and when the ball sometimes is on target then the keeper saves it."
The Bavarians have won just one of their last five matches in all competitions, scoring a total of four goals with none of them coming from their strikers.
Bayern know that if they are to rescue their season with a record-extending 11th straight Bundesliga title and take some pressure off the club leadership they have to start scoring again on Saturday at Mainz.
"We can build on the energy we have but we know that on Saturday Mainz will be waiting for us and they have had a week to prepare," Muller said. "This is now our main focus, not to dwell too long on this bitter elimination (by City)."
Mainz will be no pushovers, having gone nine games without defeat in the Bundesliga - longer than any other team currently - to climb to eighth and challenge for a European spot.
Dortmund have to make amends for last week's slip-up in a 3-3 draw at VfB Stuttgart after leading 2-0 and 3-2 in stoppage time. On Saturday, they host Eintracht Frankfurt who are without a league win since mid-February.
