Gary Warren headed Caley Thistle into a 42nd-minute lead after they dominated 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.
Boss Wright, who revealed Frazer Wright had sustained ankle ligament damage in a first-half incident that saw him carried off on a stretcher, bemoaned Hasselbaink's miss, saying: "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
- Nigel Hasselbaink
- Frazer Wright