Coyle's first game at the helm since moving from Burnley also ended in defeat against the Gunners, 2-0 at Turf Moor on Sunday.
Bolton remain deep in trouble, second from bottom of the table.
However, defender Robinson insists the mood in the camp is positive for the challenges ahead.
"We deserved better and we are disappointed not to have got anything," he said on the club's official website, www.bwfc.co.uk.
"Arsenal are a top side, but we gave them a run for their money - twice.
"We have a lot of confidence and there is a real good spirit about the place - the gaffer has given it a real buzz."
Robinson added: "He wants us to play good football and show what we can do, and it has been great how the fans have been right behind us.
"The gaffer wants us to play free-flowing football and we showed against Arsenal that we can do that against the best teams.
"The confidence is there in the group of players that we can pick up points and get out of the position we are in after the last two performances.
"We will be taking our frustrations out on any team that comes in front of us now."
Arsenal defender William Gallas will not face retrospective disciplinary action from the Football Association following his late tackle on Mark Davies.
Coyle labelled the challenge, which happened in the build-up to Arsenal's crucial equaliser at the start of the second half, as "akin to assault".
Robinson felt for his team-mate, telling the Bolton Evening News: "It was a disgusting tackle.
"He's lucky he hasn't broken his leg."
Barclays Premier League Relegation 2009/2010 Win Outright: Bolton 11/4