The Hammers' striker says he always dreamt of scoring at Wembley and to get the goal that helped send his side back up to the Premier League is "an immense feeling"
Cole gave the Hammers a first-half lead which was pegged back by Thomas Ince early in the second but a late Ricardo Vaz Te strike made sure the east Londoners returned to the top flight at the first time of asking.
The 28-year-old said he had always wanted to score on the hallowed turf of Wembley Stadium and was delighted to make his boyhood dream a reality.
"It's the best feeling in the world. To be back in the Premier League this way, you just can't ask for much more. The lads are superb, all season, and it's more than what we deserve," he told Sky Sports.
"We had to deal with the pressure and we did today" - Cole
"I thought we could have played a lot better. But it doesn't matter how you play in a final. You've got to just turn up and put the ball in the back of the net. That's what we did today, just scored more goals than them.
"It's the best feeling in the world [to score at Wembley]. I always wanted to score goals at Wembley as a kid, to do it on my first start at Wembley is an immense feeling."
West Ham narrowly missed out on automatic promotion after finishing third in the Championship with many labelling the Hammers as favourites to win the league.
Cole believes Sam Allardyce and his team-mates have done well to deal with the pressure this season and that they, along with the club's fans, deserve their place back in the top flight.
"[The pressure at the start of the season] is what we got dealt with," he continued.
"Obviously, we were the favourites to win the league at the start of the season, but that burden on your shoulders - Sam has done brilliantly to get the boys on a level playing field and say, 'Listen, we know everybody sees us as the favourites', even coming into the game today.
"We had to deal with the pressure and we did today.
"I'm looking forward to [the Premier League]. I'm so happy for the players and everybody connected to the club. The fans, that's what they deserve. We went down in difficult circumstances last year, but to come back at the first time of asking is more than enough."