Arsene Wenger has accepted Arsenal have little chance of winning the title now as they sit nine points behind Manchester United with four games to play.
Arsenal fell behind to a Daniel Sturridge goal in the first half, but the game looked to be turning in their favour after the break when Kevin Davies missed a penalty before Robin van Persie levelled the scores.
However, the Gunners were unable to take their chances and were punished late on when Tamir Cohen headed home the winner for Bolton.
"It's hard to lose a game like that," Wenger told Sky Sports. "We gave everything. Our attitude was fantastic. We were 1-0 down and had chances to win it.
"We have to give as much as we can until the last game, but of course the chances are minimal now. The players fought very hard and the players are disappointed."
It was another frustrating match for Arsenal, whose form since the Carling Cup final defeat to Birmingham has cost them dear.
Over the last week, Arsenal have conceded leads to both Liverpool and Tottenham but, despite this latest setback, Wenger is not considering drastic changes.
"I feel this week we could have taken nine points and we have taken two," he said. "We do not have to change our way of playing.
"I feel we have to be more mature in some situations when we are looking too frail. If you look at the way we dropped points it makes it even more frustrating."
Bolton boss Owen Coyle said the victory was important as the players felt the need to make amends for the 5-0 FA Cup semi-final defeat to Stoke in their last outing.
"The boys have been magnificent all season," he said. "We had one terrible, horrible day last week when everything that could go wrong went wrong.
"We didn't feel great about ourselves and that will stay with me till the day I die, but today I think everybody has seen the true Bolton.
"Every one of them worked their socks off. I'm absolutely delighted to get the late winner."
Sturridge added: "We're just delighted to come out here and work hard. After last week's result we wanted to come here and show the fans we had the passion.
"A lot of fans were very unhappy with last week - we did this for the fans today."
After his winner, Cohen unveiled a T-shirt bearing an image of his father, Avi, who died in December after a motorbike accident.
"I came on to protect the 1-1," Cohen said. "I am very happy to score this goal - it's been a very emotional season for me. I am happy we won and collected another three points."