Materazzi, who was an unused substitute as Inter oin 3-2 to progress to the quarter-finals of the Champions League on the away goals rule, angered Schweinsteiger with his conduct at the Allianz Arena.
Though the specifics of his offending behaviour are unknown, Schweinsteiger says he can sympathise with Zidane, who headbutted the defender in the 2006 World Cup final after he insulted the Frenchman's family.
"I understand how Zidane felt," Schweinsteiger said. "The Inter defender did nothing but try and provoke even from the dressing room. It wasn't the right behaviour,"
Inter, though, were ecstatic with the victory which was achieved by a well-taken goal from forward Goran Pandev in the last two minutes. The Nerazzurri became the first team in 15 years to progress after losing the first leg of a knockout tie at home.
President Massimo Moratti was full of praise for coach Leonardo, who was appointed in December to replace Rafa Benitez and has overseen a rejuvenation in the club's league form that has taken them to within five points of leaders Milan.
"I would give a ten (out of ten) to Leonardo," Moratti said. "This was a very tough game from a psychological point of view and he was excellent.
"This team has personality, character and is very united. Even when things go badly, this team is able to turn things around and that is also the merit of Leonardo. We controlled the game in the second half and once the team again felt sure of itself, we took the win home."
Leonardo added: "This is an historic win. You can have good or bad times but what happened in Munich is a sign of what Inter can be."
Inter had to overcome an error from goalkeeper Julio Cesar for Bayern's first goal. The Brazilian was also at fault for the goal Inter conceded in the home leg and walked home from San Siro that night. However, he said he was moved to tears by Pandev's winner.
"It was a truly horrible moment," Cesar said of Mario Gomez's goal. "When I conceded that goal I wanted to walk off the pitch straight away and go back to Milan - on foot, on horseback, anything. But then I recovered.
"The goal was like a cold bucket of water over my head, but thanks to my team-mates we got back on track and I really must thank them. Without doubt my mistake was worse than in the first leg, but fortunately we are still here commenting on a victory.
"When Pandev scored, I started crying. I thanked God and all my team-mates. I would've been far too upset if we had gone out because of my mistakes, but these things do help you to grow. Here's hoping I've used up all my howlers for this season."