"I don't ever want to see a player sent off but Lee was on a yellow card and clearly caught Johan and was nowhere near the ball," Coyle told the BBC.
Sunderland manager Steve Bruce admitted they might have "got away with one".
Cattermole's booking in the first half for a foul on Stuart Holden was his fifth caution of the season and means he will be suspended for the away game against Manchester United on Boxing Day.
Best save I have seen from any keeper for a long long time
MackemsRule
However, it could have been even worse for the tough-tackling Cattermole, who has already been sent off twice this season, with Foy opting against a card for bringing down Elmander on the halfway line.
Bruce believes the official decided to show lenience to his midfielder for the first-half booking that both player and manager disputed.
"I think the first one was harsh," said Bruce. "Maybe the second one he has caught him and the letter of the law says he could have gone, but maybe Chris thought the first one was innocuous and maybe we have got away with one. Maybe it evened things up."
Bruce saw his side move up to sixth in the Premier League table with the win, courtesy of Danny Welbeck's first-half header.
Welbeck also hit a post but Bolton also had chances late on to take a point away from a bitterly cold Stadium of Light and were also denied by a wonder save from Craig Gordon to keep out a Zat Knight shot.
The victory sees Sunderland move level on points with Tottenham and approaching the halfway stage of the season they currently sit in a European position.
Sixth-placed Sunderland delight Bruce
"One thing I have learned is to never get carried away," added Bruce. "We have a good squad of players. I have said all along getting in the top 10 is the aim and that remains so.
"Who knows? Come spring we could mount a challenge and to get European football here would be great."
Bolton slipped to seventh but Owen Coyle was happy with their efforts and is hopeful he can bring in some fresh bodies in January to bolster his squad.
"We showed we're a decent team again," added Coyle. "We only had 19 players available but every one of those players is quality. It'd be nice to freshen things up and help the group I have got - we'll have a look about and see what's there.
"I've got my eye on one or two. We need more than funds for it to happen; we need the desire of the player to come for a start."
Source: BBC Sport
Source: BBC Sport