Caley Thistle were formed only 21 years ago and have enjoyed their best season to date, finishing third in the Scottish Premiership and now picking up a first major trophy.
The Highlanders opened the scoring through Marley Watkins but they had defender Carl Tremarco dismissed 15 minutes from time as he tripped Blair Alston as the Falkirk midfielder raced clear towards goal.
Falkirk had already been pushing Caley Thistle back throughout the second half, and were level five minutes later through Peter Grant, but substitute James Vincent snatched the winning goal on the counter-attack on 86 minutes.
“We’ve made history once again, winning the Scottish Cup, absolutely fantastic,” Hughes told Sky Sports 3.
“I’d like to pay respects to Falkirk, they were the better team in the second half and somehow we’re down to 10 men but we’ve pulled through again.
“I felt we started a little bit nervous but then got going and got a good goal.
“In the second half we never turned up but the spirit to turn it round and win it was exceptional.”
Hughes, who has also been voted manager of the year in Scotland, concedes it may be a tough task to top the success at the club this season.
“I don’t think you can, but what we have done is set standards at the club that we have to maintain,” Hughes said.
“They’re a wonderful bunch of boys and they’ve got real team spirit amongst them and I think that showed even when we were up against it second half, we still dug it out.”
Inverness skipper Watkins, who scored the first and indirectly set up the second for Vincent, felt the chance of silverware was slipping away from his side after they were pegged back to 1-1 and with 10 men.
“I thought, honestly, oh my God. We never do it the easy way so once that goal went in – although I think I should have passed it before I shot to Vinny – I was just over the moon,” he said.
“I was watching the clock all the time and waiting for it to go. It’s an amazing occasion.”
Watkins has been strongly linked with a move to newly promoted Hearts this summer, and when asked if the cup win would be the perfect way to sign off at Inverness, he said: “Yeah, it’d be the best way.”