Blues fans were in full voice last night as they chanted Mourinho's name throughout the game.
Schwarzer said: "Every opportunity they had, they clapped the manager. They cheered him. The manager responded as did the players. It lifted the team.
"It would have been very emotional for him. He would have been touched by it. He's a very emotional person. Anyone would have been affected by what's happened this season and to have that support from the fans would be very special for him. He'll use that. He'll build on that and gain confidence from that. The team will also flourish from that.
"There's nothing worse than going out on the pitch when the fans are on edge. But there was none of that tonight. The supporters were behind the team and the manager."