The Gunners looked to have gone some way to recovering from the 6-0 trashing at Chelsea when they came from behind with two goals in as many second-half minutes to lead Swansea 2-1 at the Emirates Stadium on Tuesday night.
However, a calamitous own goal from Flamini in the last minute of normal time - when the ball was partially blocked by defender Per Mertesacker, only for it to ricochet off goalkeeper Wojciech Szczesny and back onto Flamini before rolling into the net - saw the relegation-battling Welsh side leave with a share of the points.
Arsene Wenger's beleaguered squad must now lift themselves for the visit of a rampant Manchester City in Saturday's late afternoon kick-off, where defeat would all but end any remaining Barclays Premier League title ambitions and also allow Everton to crank up the pressure in the fight for a top-four finish.
"The team spirit is still here and we gave a good example because coming back to 2-1, we were holding the result until near the end, so it was a good reaction for the team," said Flamini, who had been recalled to the starting XI by Wenger.
"Obviously, it will be very difficult to win the league now because we dropped three points at Chelsea and another two here.
"It will be very difficult, but what is important is to focus on the next game because we have to get a good result and then we will see."
Flamini added: "We want to do well, especially after the big loss against Chelsea.
"We want to prove that we are one of the big teams in the Premier League."
Wenger has seen his midfield options hit by injuries to key men such as Theo Walcott, Jack Wilshere, Aaron Ramsey and Mesut Ozil, while defender Laurent Koscielny is also set for a spell on the sidelines with a calf problem.
Captain Thomas Vermaelen, however, maintains such issues just have to be dealt with.
"I don't think that is an excuse," said the Belgian defender, who replaced Koscielny at centre-half against Swansea and was outmuscled by Wilfried Bony as he headed Swansea in front on 11 minutes.
"We have a big squad with good players, so that shouldn't be the reason.
"I don't know if there was any lack of confidence in the team.
"We were pushing the whole game but it was difficult to score."
One positive at least was a late substitute appearance by Sweden midfielder Kim Kallstrom, who finally made his debut following a back injury after signing on deadline day in January.
"For me, it felt really good coming on. I had a lot of time with the ball, I had some clean passes. I was involved and I am just pleased to be out there playing," he said to Swedish newspaper Expressen.
"It is a very high level and I'm really looking forward to contributing to Arsenal.
"It is high speed and tough play, which I like."
Wenger had called for a response to the "accident" of Arsenal's capitulation at Stamford Bridge which ruined his 1,000th match in charge.
The manner of the way Swansea were let back into a match which Arsenal should have closed out for what would have been a morale-boosting victory has again seen the character of his side questioned.
Wenger, though, will continue to focus on the job in hand rather than concern himself with any negative headlines or broken cannon motifs.
"We live at the moment in a permanent assessment from everybody and the definite judgement. We always have to let people judge, assess, criticise. We find plenty of people who can do that I don't worry about that too much," said Wenger, whose side are in the FA Cup semi-finals, but as yet has not signed a new contract offer.
"I just do my job and focus on the next game and let people assess and judge. They know much better than I do so I leave them the job."