Bayern missed a glorious opportunity to win the title for the first time in 11 years and Nerlinger expects it will now take a while for his side to get over the loss, which ensured a second successive trophyless season for Germany's record league champions.
"To sum it up, it is a nightmare which we have experienced," he said.
"It is like a bad film. We totally dominated Chelsea and did not let them have any chances.
"We fought and battled and created chances and when you take the lead in the 83rd minute, then the game is basically over.
"But then you concede an equaliser from the only chance from a corner in the game, and then you lose on penalties, what more can I say?
"We had plenty of match points, we just did not take them.
"We were clearly the better team, but sadly we have lost and that is the reality."
Bayern captain Philipp Lahm was also at odds to explain a defeat which he felt defied logic.
"I think we have seen here that football is unfair," he said.
"We were the better team for 120 minutes and only let them have their first chance in the 88th minute after missing a hatful of chances ourselves, and that makes it even more bitter.
"It was a blow to concede in the 88th minute, but we got back going again in extra time only to suffer another blow with the penalty miss, but then we got back going again.
"I think the team reacted well to these blows and when you are so superior, then you have got to win.
"Of course only one team wins a penalty shoot-out and it was not our turn."
Lahm feels his turn will still come, though, as he has vowed to bounce back from one of the bitterest disappointments in his career.
"I so wanted to win the cup," he said. "But if we can take anything positive from this game then it is that we are in our footballing prime and the core of this team still has three or four years together and we are hungrier now that we did not do it.
"But it is tough as we wanted to win it so much, yet we are left empty-handed.
"Not always the best team wins, I've got to say.
"We did not fully pay attention from just one corner, and we have lost the Champions League."