Ivan Klasnic spared Wanderers' blushes with the only goal in their second round tie at St Mary's on Tuesday night.
The Croatian was handed his first start since rejoining Wanderers in the summer as one of nine changes made by boss Coyle.
And Klasnic, who hit eight goals last term while on loan from Nantes, sank League One Southampton with an opportunist first-half strike.
Coyle was also indebted to Hungarian youngster Adam Bogdan, who was given his debut in goal and produced a string of fine saves as Bolton, with an eye on Premier League survival and just Kevin Davies and Zat Knight surviving from Saturday's win at West Ham, avoided a shock.
"We made nine changes from Saturday and that was for two reasons," said Coyle.
"One to get a bit of freshness and also to give these lads some game time under their belts because they will all be called upon in the Premier League.
"It was a hard-fought game and tremendous credit to Southampton. They were terrific on the night but we are delighted to get the victory."
Rookie keeper Bogdan kept the top-flight side in the game in the first half an hour with fine saves to deny Adam Lallana, Jason Puncheon and the pick of the bunch from Lee Barnard as the forward raced through.
And Saints found themselves behind on the half hour, when former Southampton striker Davies knocked down Sam Ricketts' cross for Klasnic to prod home.
"I thought it was the toughest draw we could have got - a really tricky game and so it proved," added Coyle.
"Adam pulled off a couple of big saves for us and we had to score a terrific footballing goal ourselves.
"The goal was from the Premier League. Sam Ricketts beat a couple of players, it's an exquisite cross, the skipper does what he does best and it's a terrific finish from Klasnic."
Such is the standing of this competition, especially the early stages, that Saints also have bigger fish to fry this season and will not shed too many tears at bowing out.
Alan Pardew's side are favourites for promotion this term, and although they have not managed a win in League One so far they dominated Wanderers for long periods.
"I thought anyone who was here tonight would admit we were unlucky to be beaten," said Pardew.
"We are having one of those spells where we just can't seem to capitalise on the chances we are making.
"There were some great performances but we just couldn't get a break."