Lewis McGugan gave Forest a 15th-minute lead courtesy of an unstoppable 30-yard drive and the visitors were far superior in the opening half hour.
Chris Eagles levelled for Bolton after Kevin Davies' header came back off the post and when the veteran striker pounced on an error from Greg Halford he set up Marvin Sordell to put Coyle's men ahead early in the second period.
But Andy Reid found a sumptuous finish of his own following good work from Dexter Blackstock and Simon Cox to put Forest on terms once more before the hour.
Having acknowledged the excellence of McGugan's strike, Coyle stated Forest's equaliser was avoidable and bemoaned his player's profligacy after half-time.
"Truth be told we really should have put the game to bed at 2-1," he said. "The chances we had to finish the game off were real goalscoring opportunities, not half-chances.
"My frustration is that we've gifted them a soft second goal - a hopeful long ball that we could have dealt with in the centre-back position.
"Then Reid's run unmarked from the middle of the park. Fair play to him - it's a wonderful finish that he's done all his career.
"I'm frustrated because there was a lot of good attacking play from our point of view and we showed a bit character coming from a goal behind.
"On the balance of play and clear goalscoring chances I certainly felt we should have had three points in the bag."
Coyle suggested Bolton might have ended the game playing against 10 men after Forest's already-booked midfielder Adlene Guedioura tangled with substitute Benik Afobe.
"I think he had three kicks at young Afobe in the same movement," he added.
"I wouldn't want players sent off, that's the last thing we want, but the rules are there for everybody to see.
"It happened, but we're not going to hide behind that. At 2-1 we should have gone on to make that game three or four with the chances we had and certainly not gifted them any more goals."
Opposite number Sean O'Driscoll was also aggrieved, claiming Davies fouled Forest captain Danny Collins in the build-up to Eagles' goal before obscuring the view of goalkeeper Lee Camp from an offside position when the strike came in.
"It's a definite push and I thought Kevin was standing in front of the goalkeeper as well so there were two things," he said.
"I'm disappointed in that, but there's nothing we can do about it."
O'Driscoll watched his players preserve their unbeaten start to the season, but he was aghast by the open nature of the match in the second half.
"Both teams could have won it four or five - it could have been four or five to them or four or five to us," he added.
"It ended up being a five-a-side game with 22 players on the pitch, that's the problem.
"They could have scored, we could have scored. It was unreal."
