Goals from Esmael Goncalves, Steven Thompson and Conor Newton cemented the victory for Danny Lennon's men with goals sandwiched between Ryan Stevenson's double for the Jambos.
McGowan said: "It's unbelievable. I'm so proud of every one of the players and it's a great day. We truly deserved it.
"It's been coming for St Mirren, they're a great club with great fans and it's been a great day."
On his own performance, McGowan added: "They came and pressed us quite high and gave us a bit of trouble and so they moved me back into midfield and I helped us a lot there.
"It was a great day for us and I'm proud as anything.
"It's a once-in-a-lifetime opportunity to try and win a cup here and we've done it and made every one of the fans and our families proud. I can't ask for any more."
Thompson added: "It's pretty much indescribable really. I've been dreaming about doing it ever since we beat Celtic and I won't lie, I've not had a lot of sleep.
"I made a near-post run and made sure I was really concentrating to make a good connection with the ball - you could probably see from my face that it was a dramatic moment.
"It's just an amazing feeling and in the next few days I'll realise what it means.
"I'm a supporter too and it's been a quarter of a century since we won a cup so it means everything to them.
"It's great to be part of the history of this football club and I'm bursting with pride."