Klaas Jan Huntelaar and Ibrahim Afellay capitalised on slack defending to score in the final 15 minutes in the Gunners' first home defeat in the group stage for nine years.
Angry supporters left in their droves once Afellay had put the result beyond doubt and the few that remained booed at the final whistle.
With manager Arsene Wenger serving the final game of a three-match touchline ban, it was left to his number two Bould to reflect on a highly disappointing evening.
"We've lost at home and of course they're frustrated. We are as well," Bould said.
"We don't like losing football games, but we have to pick ourselves up and start again.
"We haven't played anything like we can - that was the big disappointment.
"We haven't performed and we lacked confidence, for whatever reason.
"It's a tough competition and Schalke are a good side who beat Dortmund at the weekend.
"They're doing really well and a 0-0 would have delighted us. We looked like we were going to get away with it for a long time.
"We looked jaded - I don't why that is. Since coming off the international break we haven't performed.
"We were very sharp against West Ham but since returning from the internationals we've been jaded."
Arsenal were restricted to just one shot at goal in the entire match and had to wait until stoppage time for that, with substitute Serge Gnabry producing a late attempt.
But their failings in their own area were more damaging with both goals - just reward for Schalke's second-half dominance - exposing a fragile defence.
"The lack of chances isn't worrying, but it's not what we want or are accustomed to," Bould said.
"We normally create chances and now we're not, so we need to correct that.
"Their first goal was a poor goal - a great finish, but it wasn't great for us.
"Scoring first will be a major plus for us. We've gone behind in the last five games. To keep coming back is tough. An early first goal would really help."
Schalke now top Group B, one point above Arsenal with three matches left to play, and Bould promised an improvement against the German club on November 6.
"There are nine points left to play for. Wherever we get those points from it doesn't matter, but I'm sure we'll perform a damn sight better than tonight [Wednesday]," he said.
Bould revealed Theo Walcott will miss Saturday's Barclays Premier League clash with QPR due to his bruised lung.
However, Alex Oxlade-Chamberlain is back from a hip problem while Jack Wilshere should be available for selection.
Schalke manager Huub Stevens took no satisfaction from masterminding Arsenal's first group defeat in Europe since Inter Milan prevailed 3-0 in 2003.
"For me it's not important how Arsenal are playing, but how Schalke are playing," he said.
"Records are not important for me. For me it's important that the team is playing well.
"In the first half we didn't play well. In the second half we played a good game. We deserved to win 2-0."