Gundogan’s brace earned Man City only their second domestic Double, and the Premier League champions can match United’s historic feat of a Treble in 1999 if they beat Internazionale Milano in the UEFA Champions League final in Istanbul on 10 June.
“We have a chance to do something special and win the treble and we do not want to let this opportunity pass us by," Gundogan said. "I can promise our fans we will do everything we can to win in Istanbul.”
Gundogan put City ahead at Wembley with a tremendous volley after only 12 seconds for the fastest goal in FA Cup final history.
"The ball landed perfectly for me and I hit it first time... It was an amazing finish!” he said.
"It just placed amazingly for me and I just had to hit it. Obviously it was a quite good strike.”
“To win a final is always special,” the German said. “Every trophy is special. This group deserves it. We played really well, second half was amazing and we deserved to lift another trophy.”
'Nothing is decided on my future'
He also played down talk about his future as he is out of contract at the end of the month.
"I don't need these kind of days to feel appreciated and feel special in this club,” said a player who was Pep Guardiola’s first signing at City in 2016. “I know that and that is why I have been here seven years.
“Nothing is decided yet, we will see what will happen."
'Grealish - Stuff of dreams'
"Unbelievable,” he told the BBC. “It's stuff you dream of when you're a little kid. I was desperate to win one at Villa and now I've done it.”
"The best thing about this team is we have a mix of everything. Everyone is confident, we've got older more experienced lads and the younger lads are learning too.
"We'll have a good night tonight and then straight back at it on Sunday and Monday for a big game next week."
His manager, who did not hide his emotions at full-time, also started to turn his thoughts towards Istanbul in a week’s time.
"We can now talk about the treble,” Guardiola told the BBC. “Of course, we still have to win the Champions League.
"Tomorrow and the next day they can have off. We've then got three or four sessions to train for Inter Milan. We'll travel on Thursday morning after training.”
"We have to win the Champions League to be recognised like the team deserves to be recognised"
Guardiola admitted that his team need to win the Champions League to merit being called a great side.
“Everybody knows it," he said. "We have done incredible seasons – five Premier Leagues, two FA Cups, Carabao Cups, but we have to win the Champions League to be recognised like the team deserves to be recognised.
“We have to admit it, without the Champions League – it has been amazing, it has been fun – but we are missing [something]. We have to do it.
“We are one game away. I would say it is incredible, remarkable, that in three years we have had two finals and one semi-final of the Champions League. But in the end we have to win it.
"I know how it works. I said to the players, ‘You have to put the pressure on yourself. To be recognised as something good you have to win in Europe.'"