The victory capped a remarkable turn around in fortunes for Spurs under the Spaniard, who replaced Martin Jol at White Hart Lane just four months ago.
Spurs showed plenty of their new-found fighting spirit to recover from a first-half deficit after goalkeeper Paul Robinson was caught out of position by Didier Drogba's free-kick.
They regrouped for the restart, and following a tactical change when the versatile Tom Huddlestone was sent on for defender Pascal Chimbonda, Spurs were able to level.
The equaliser came from the penalty spot through Dimitar Berbatov after referee Mark Halsey consulted with his assistant and decided Wayne Bridge had handled inside the area.
Ramos, though, also had a slice of good fortune when, at the beginning of extra-time, Chelsea goalkeeper Petr Cech saw his attempted punched clearance bounce back into the net off the head of Jonathan Woodgate - who was the Spaniard's main signing of the January transfer window.
The victory secured a first piece of silverware for Tottenham since they lifted the League Cup back in 1999, a fact not lost of the new manager.
"It is tremendously satisfying to get the trophy, especially for the club and the fans. It has been a long time since success like this," Ramos said.
"For a club like Tottenham Hotspur, such as long time seems longer, so it is tremendous. Success always comes for everybody - for the players first as they are the ones who carry out the work we do.
"It is not a personal battle [between coaches] - it was simply that Spurs were the better team on the day."
The former Sevilla manager has brought his winning formula for knockout competitions with him from Spain.
He continued: "It is always tremendously satisfying to win a trophy. This one maybe has a special flavour because was against a team which was supposedly superior to us, similar to when Sevilla played against Barcelona and Real Madrid.
"Perhaps it makes the whole thing taste better. This has been a unique experience and one we hope to repeat.
"For the moment we will enjoy the victory. Next week we are back in the Premier League and we have to concentrate on that, we are also still in the UEFA Cup. So it is a case of little by little, but we will see. We are all calmer now that we have qualified for Europe again, which takes some pressure off the club."
Ramos also admitted he believes that his Spurs side are moving in the right direction.
"The team has been improving in terms of the security and confidence they feel. Today has reaffirmed that," he said. "The players have shown they can concentrate to be serious enough to fight with the best of them.
"The key is not making mistakes and they showed they could concentrate on that."