The Spaniard joined his team-mates for Tuesday's victory parade as the city turned out in force to welcome home their heroes.
It was all a far cry from Rangel's arrival at the Liberty Stadium.
The 30-year-old right-back is one of the club's longest-serving players, having joined in 2007 - paying part of his own transfer fee - with the Swans still in League One and Roberto Martinez at the helm.
Martinez and chairman Huw Jenkins told Rangel they were planning on taking the south Wales club into the Premier League within four years, a goal they delivered on when promotion was secured in 2011.
Swansea's upward climb has continued with the consolidation of their Premier League status and Sunday's 5-0 thrashing of Bradford, and Rangel has been as amazed as anyone by their rapid progress.
He told Press Association Sport: "When I arrived they told me in four seasons they wanted to be in the Premier League.
"I did not believe it was possible, it seemed impossible, just like a dream.
"Here we are six seasons later and we are established in the Premier League, we have won this cup and are in Europe.
"It shows how well run the club is, we have great characters and we need to keep that to succeed."
In holding a place in the top half of the Premier League table and winning a cup, Swansea are probably pushing the envelope of what may be ultimately possible for a club of their size to achieve.
But Rangel insists this is no time for resting on any laurels.
He said: "This has been a fantastic day, a fantastic feeling. These are days everyone with the club has to enjoy and a lot of people here deserve a lot of credit.
"Over the last few years we have been always climbing, but we must not get carried away, we must keep working and hopefully we can keep doing well and do something special in Europe.
"It will be difficult but if we keep our best players and the manager, I think we can do well.
"It's a chance to show we can play good football against all kinds of teams, with different tactics and we are looking forward to it."