After 120 minutes without a goal, the Dons edged out Inverness 4-2 on penalties to claim their first piece of silverware in 19 years.
Although disappointed at missing out on winning at Parkhead, Hughes told Sky Sports News: "There's no finger to point at anyone.
"We were organised, had a good game plan and our team shape was very, very good.
"Although we should have been a little bit better on the counter attack and given quicker support to Billy McKay - which wasn't the case.
"But to take on a club the size of Aberdeen and silence the supporters the way we did and take them to penalty kicks, you could have been talking to the winning manager - but unfortunately that's football."
However, Hughes believes his side should have been awarded a penalty late on when Dons defender Andrew Considine grappled with Richie Foran.
He added: "It might have been a different outcome because I felt we were denied a stonewall penalty.
"It was a stonewaller, even from where I was in the dugout. You saw the reaction of my players, so that was disappointing.
"It is not sour grapes, I give all credit to Aberdeen and we rode our luck a bit when they hit the post but when it is a penalty, simple as that.
"It would have changed the game, I think we would have gone on to win it.
"But when it goes to penalty kicks it is anyone's match. I am disappointed for the boys but so proud of them. It could have been our day."