With Kenny Shiels serving the first of a four-game touchline ban, Nicholls was the man in charge and saw his charges take the lead just before half-time.
Liam Kelly netted from the spot after Jamie Langfield had brought down Borja Perez, with the goalkeeper shown a red card for being deemed to have denied a goalscoring opportunity.
"It was a great run from Borja Perez and he kept on going. I thought he had over-run it. It's hard to say, and I've not seen the replay so I can't say whether it was a penalty or a red card or not. That was a wee break," Nicholl said.
"We weren't doing too badly. The way things have been recently, we wanted to keep it tight. It probably sounded negative to the players, but we we're just hoping to come up here and have a decent performance, and hopefully take something from the game."
Aberdeen boss Craig Brown refused to be drawn on his view of the Kilmarnock spot-kick, but felt it was the turning point in the match.
"The first goal was a defining moment, and it became difficult for us," he said.
"However, in the second half you would have thought we had the extra man because we were dominant, although Cammy Bell only had one real shot to worry about, the one from Magennis that came off the crossbar.
"It's a major disappointment to suffer a home defeat, especially after our performance on Tuesday night. I think there was some reaction to Tuesday night, and we had no experienced players to freshen the team, with seven players out injured.
"Particularly in the early part of the game, you could see we were suffering, but we got a second wind in the second half until we lost the second goal. It seemed the most unlikely thing in the world, because our replacement goalkeeper, Jason Brown, didn't have a thing to do."