Lewis McGugan's thunderbolt gave Forest a 15th-minute lead before Chris Eagles levelled and Marvin Sordell put the hosts ahead, 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 players' profligacy after half-time. He said: "Truth be told we really should have put the game to bed at 2-1. The chances we had to finish the game off were real goalscoring opportunities, not half-chances."
He added: "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 of 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."
Opposite number Sean O'Driscoll was also aggrieved, claiming Kevin 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. He added: "Both teams could have won it four or five - it could have been four or five to them or four or five to us. It ended up being a five-a-side game with 22 players on the pitch, that's the problem.