Schweinsteiger missed Bayern's last penalty in Saturday's shootout, and Didier Drogba then stepped up to score with Chelsea's final shot.
Photos showed Schweinsteiger walking past as German President Joachim Gauck held out his hand. The player says he didn't refuse the handshake.
Schweinsteiger says in a statement released by Bayern that he felt "paralyzed" after missing the penalty.
He says "at that moment, after this great disappointment, I noticed nothing around me any more ... I didn't see the president's hand."
He adds he is "sorry that this moment allowed a different impression."