Fabregas, who joined Arsenal as a 16-year-old from Barcelona in 2003 and has turned into one of the best midfielders in world football, moved back to his boyhood club on Monday.
"We have lost a world class player and we are sad about it, we did try to keep him," Wenger told a news conference ahead of his club's Champions League playoff first leg against Italians Udinese at Emirates Stadium on Tuesday.
"In the end we had to respect the desire of the player. This club is 125 years old this season and many big players have left the club and the club has gone on. So we want to show we have the strength and the unity to fight as ever."
He added the move made sense for Fabregas for many reasons.
"He comes back to Barcelona, he was educated at Barcelona. His grandfather was part of the [club] committee," Wenger said in his native French.
"He was virtually brought up at Barcelona's creche. On top of that, he is going to a club that has the best team in the world at the moment.
"So from that point of view, we can also understand that it has nothing to do with money, it is an affair of the heart."
At the same time Wenger was speaking, so was Fabregas who praised his former manager in front of the Spanish media.
"I'll never have enough words to say what I think about Arsene Wenger and if Arsenal wants to be the club they are they always have to be under his control," the 24-year-old said.
"He is the best, everyone respects him and he will always be the best person I met in football. He was like a father figure to me. If today I am here with you, living my dream, then it's greatly due to him."
'BIGGEST REGRET'
Fabregas added he was sorry he had not been able to tell fans what was happening, explaining Arsenal had effectively gagged him from speaking about the situation.
"My biggest regret is that we won only one FA Cup and the biggest regret I will have in my career is that I did not lift a trophy as an Arsenal captain, but I am sure they will be a strong team again," he added.
"I will always be an Arsenal fan because what they have done for me is unbelievable and I will never forget it."
Losing Fabregas's creativity, versatility and eye for a goal is a big blow for Wenger and his squad could be further depleted if France midfielder Samir Nasri heads off to Manchester City.
"The two things are not linked," Wenger said. "Ideally I want Samir Nasri to stay... the situation is a bit different with Samir and hopefully we can sort the situation out and keep him.
"I am encouraged by the fact we can still bring one or two players in because we are a bit short," he added, explaining the talks surrounding Fabregas's move had taken up so much time he had been unable to concentrate on prospective signings.
Wenger has been criticised by some fans for the first time since becoming Arsenal's manager
