Freddie Ljungberg gave the Champions League finalists a 29th-minute lead but David Sommeil pulled City level 7 minutes before the break, tapping home from close range after Arsenal failed to clear a corner.
The two goalkeepers, David James and Jens Lehmann, each made a number of decent saves before Jose Antonio Reyes scored twice within 12 minutes of coming on in the 72nd minute to give the visitors the three points.
Pearce felt City could have got something from the game but gave Arsenal too much space to play.
"I thought we stuck to our task quite well," he said. "Our corners, set plays and crosses flashed in quite well and we looked like scoring goals.
"I thought we afforded Arsenal a touch too much respect when they got nearer our goal. In that last 30 metres we should have got in their faces a bit more."
Still trying to snatch fourth place off Spurs, Arsene Wenger named a full-strength line-up, and besides Reyes, he also had Cesc Fabregas and Robert Pires coming off the bench in the second half.
"It's difficult for me to take anything away from Arsenal, they are a top, top outfit and one of the best sides in the world," added Pearce. "When you are chasing a game, they will pick you off, they are masters of the counter-attack.
"They are an excellent side, and probably the comparison between the two benches was a stark contrast.
"I though for patches in the game we did OK, but we should have shown a bit more belief and then we might have got something."