The Cottagers made a bid for the 27-year old Spaniard and it was believed the club had agreed a fee but Swans chairman Huw Jenkins did not allow him to leave the Liberty Stadium, which has disappointed the player.
"I will be honest, what I know from my agent is that Fulham made an offer and it was the offer the (Swansea) chairman was asking for," Rangel told the Evening Post.
"But then when everything about the deal was sorted and everything was ready, the chairman did not answer his phone or he turned it off.
"I think he asked for quite a lot of money for me and Fulham made a huge effort to get me, but he didn't want to sell.
"I think he asked for quite a high fee and he didn't expect Fulham to agree it.
"To be honest I am disappointed. We are not talking about another Championship club or a struggling Premier League club.
"I have always given my best for Swansea City, but I have always said I would like to consider it if a Premier League club came in for me.
"Swansea only paid a few thousand pounds for me so they would have got a good profit out of the deal.
"But it didn't happen and I am disappointed. I feel like the chairman has stopped me improving my career."