Flamini has been free to negotiate a move away from Arsenal since January
Arsenal boss Arsene Wenger has admitted there was only so much he could have done to prevent Mathieu Flamini's exit.
Wenger would not break his wage cap for Flamini, 24, who turned down Arsenal's reported offer of £55,000-a-week to join AC Milan on a free transfer.
"It is a problem [the salaries on offer] but we did not master this situation with Flamini," Wenger told a forum for Arsenal shareholders.
"I must say I am disappointed that he did that but legally he can do it."
Wenger, who also reiterated his desire to retain Alexander Hleb amid reports linking him with a move to Inter Milan, added: "When a player is out of contract he can sign where he wants."
Flamini became a free agent on 1 January as the combative midfielder, who joined from Marseille on a four-year deal in July 2004, entered the final six months of his contract.
While captain William Gallas is reported to earn around £80,000 and Cesc Fabregas £75,000, Wenger has said Arsenal must respect their tight wage structure or "go bust".
Following the 3-0 win over Newcastle in January, Flamini said: "My priority is to stay here.
"I'm very happy here. My representatives are talking with the club and I hope everything will be good."
If our players are not capable of doing that and just want to walk out for bigger contracts, for me that would be the biggest disappointment
And in March, Wenger insisted discussions were moving towards a positive conclusion.
"We will meet soon with Flamini and we hope to sort it out," he said. "We are on course. Negotiations are going well and we hope to sort that out in April."
But on Tuesday the Gunners confirmed Flamini would join Serie A giants Milan on 1 July, receiving a signing on fee thought to be in the region of £4m.
Since Arsenal's push for silverware this season ended with elimination from the Champions League and Premier League title race, Wenger has repeatedly stated that his prime objective is to keep his squad together.
But Jens Lehmann has not been offered a new deal, while Hleb, Fabregas, Gilberto Silva and Philippe Senderos have all been linked with moves away from the Emirates Stadium.
"I hope that 95% of the team, the core of the team, says 'come on, we have only just lost'.
"And it is just because we were leading at Manchester United, we were leading at Chelsea and we were leading at Liverpool in the Champions League - and every time we just lost a little bit of focus and lost the game.
"We were close this year, but we did not win and what I expect from my team is that, if you are a winner, you say 'let's come back next year and win'.
"If our players are not capable of doing that and just want to walk out for bigger contracts, for me, that would be the biggest disappointment."
Since Flamini's departure, speculation has shifted towards Hleb's future.
The Belarusian has been linked with a move to Inter Milan and reports have suggested the 27-year-old could invoke the a Fifa rule which allows players to leave a club after three years of a longer fixed-term contract, provided they do not move to a club in the same country.
Hleb is approaching the end of his third season with Arsenal but Wenger, who plans to report Inter to FIFA over an alleged illegal move for the player, has played down the chances of the midfielder 'buying-out' his contract.
"What people say about the buy-out clause, it is not as simple as it looks," he said. "It is much more difficult and the [buying] clubs are reluctant to do that.
"We want to keep Hleb, we want him to be part of our team next year. It is as simple as that. We have lost one player, we do not want to lose more."
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