Both the midfielder and his coach, Pep Guardiola, acknowledged that the Bavarians struggled in the first half at the Coface Arerna before improving after the break
The Bavarians struggled to break down their hosts but finally made the breakthrough with eight minutes to go through the 29-year-old Germany international.
Mario Gotze sealed an 18th consecutive Bundesliga win for the visitors but Schweinsteiger was the first to admit that Pep Guardiola's men had been made to work harder than usual for the three points.
"Victories in Mainz are always hard-fought," the midfielder pointed out. "This is a very aggressive team, with a very great ability to press.
"It was not easy in the first half. But in the end they were tired. We wanted to maintain our rhythm and the second half was okay."
Bayern boss Guardiola also admitted that the reigning European champions had struggled to get going during the opening 45 minutes.
"In the first half, the game kept going back and forth," the Spaniard confessed. "In such a game, we have a few more problems than usual; it's not easy.
"But during the second half we played better and controlled the game."
Bayern could have clinched the title with a win at Mainz but Borussia Dortmund's victory at Hannover ensured that they will have to wait at least another round before they can start their celebrations.