The Highlanders, who will face Aberdeen in next month's League Cup final, earned just the third victory of Hughes' reign courtesy of a first-half header from Gary Warren at McDiarmid Park.
However, Hughes believes his side, who are seven points adrift of second spot with two games in hand on Aberdeen, will find it difficult to rein in the Pittodrie outfit.
He said: "Can we catch Aberdeen? I don't know, it depends what we do, it depends if we can keep winning football matches.
"But I very much doubt it. I think it will be Celtic and then Aberdeen, but as long as we stay in the mix I'll be happy.
"One thing I will say is that we don't want to sit back and rest on our laurels, in terms of being in a cup final and still being in the Scottish Cup.
"The league campaign is our bread and butter, I feel that's where you get judged, and so to come here and pick up the victory, I'm absolutely delighted.
"There's something in the water up in Inverness, I'm serious. With this bunch of boys in that dressing room, there are no egos, no Billy big times.
"If they play good, indifferent or bad, you know you're getting 100 per cent. They train like that, they play like that, they live their lives like that.
"They're all in it together. We just take it as it comes. We've got a big game on Tuesday in the Highland derby and we're looking forward to it."
Inverness fully merited Warren's 42nd-minute goal after dominating the first half - but they came under more pressure from St Johnstone after the break when Nigel Hasselbaink should have scored with a header from the ricochet off a Dean Brill save.
However, Hughes believes Caley Thistle were deserving of their victory in the end.
He added: "I think we were worth the win. In the first 10 minutes we could have been a couple of goals up.
"We got a little bit lucky in the second half when they missed a header just past the post; the boy should have scored.
"In the second half there was plenty of rearguard defending, plenty coming into our box - but when you've got guys like (Josh) Meekings and Warren going to head it, (Ross) Draper back in there screening and your goalie coming to catch it, it needs to go in with quality.
"And I don't think there was enough quality going in there for us to lose a goal."
St Johnstone counterpart Tommy Wright bemoaned Hasselbaink's miss but, revealing Frazer Wright had sustained ankle ligament damage in a first-half incident that saw him carried off on a stretcher, was adamant his team deserved to snatch a draw with their improved performance after the interval.
Wright said: "We should have got something out of the game, particularly in the second half. We controlled large parts of it and we had the best chance of the second half.
"But we didn't start the game well, even from the kick-off, which was a disaster for us, and we didn't win enough tackles in the first half, or second balls.
"A little bit of indiscipline and some crazy decisions at times allowed them a lot of free-kicks and they put us under pressure by putting a lot of balls into the box.
"But we should have got something out of the game because in the second half we were much better than them.
"Nigel's had a good game and he was in the right place, but I think it just came at him a little bit quick and I don't know if he was stretching for it.
"That was the best chance in the game and it summed up our day."
- Sports & Recreation