The Swans beat Bradford City 5-0 in the final at Wembley Stadium on Sunday, to cap a remarkable 10 years which has seen them gone from narrowly avoiding relegation from the football league to an established Premier League side.
The Spaniard is delighted that the Welsh club have also earned qualification for European competition for next season.
"I'm so proud of the team," Rangel told talkSPORT. "If you told me six years ago that I would be playing in the Premier League with Swansea City and winning a cup final, I wouldn't have believed you.
"Today was obviously a fantastic day, but not only today, the whole season so far. Being in the top 10 of the Premier league and winning a cup final is the biggest achievement Swansea can get. We're in the Europa League next season as well, which is a missive thing, and we knew that we had a good chance to get there through the Capital One Cup.
"We had an opportunity and we took it. We were up for it and it was well deserved."
Rangel is currently playing in his sixth year at the club.