Caley Thistle were down to nine men and losing 2-1 to Hearts when Nick Ross spun to poke home the equaliser deep into stoppage time at Easter Road.
They went on to hold out for the 30 minutes of extra time before Ross Draper shook the cramp from his legs to nonchalantly tuck away the winning penalty and book a final date with Aberdeen on 16 March.
"It is nothing to do with me. It is these boys and all we do is try to organise them," said Hughes, who was taking Inverness to their first major Cup final.
"Someone up there likes me and the boys thoroughly deserve it.
"I have to say I don't think Gary Warren's first one was a yellow card and I don't think Josh Meekings was a red card. It could make it a bit of a lottery in the final with our two centre-halves missing."
Inverness goalkeeper Dean Brill, who saved two penalties in the shoot-out, said: "It was nine versus 11, people out of position, backs to the wall, but the boys stuck at it and what a brilliant finish.
"For a goalkeeper, the pressure is off in penalty kicks and we said before it - what will be will be. It is massive for the club and a bit of history.
"It was hard for the fans to come so far to make the kick-off and it's great for them.
"No fears, it is a cup final. We have had three tough games against Aberdeen, but we're really looking forward to it."
Hearts had beaten Inverness on penalties in their League Cup semi-final last season, and manager Gary Locke said: "It is very cruel, but we've only got ourselves to blame. We had the ball in the corner with a minute to go and, instead of keeping it there, we lose it and they go up and score.
"It was a great opportunity to get to a final. In extra time, we had to move the ball quicker and in wide areas. It was a very sore one to take. If we had just seen the game out, we'd be in the final right now.
"We did great to get ourselves back in the game and should have seen the game out. We got the better of Inverness on penalties last season and it's their turn now."