Evans was sent off 15 minutes from the end of Manchester United's 1-0 win over Bolton after Holden sustained a nasty gash in a tackle with the Northern Ireland international.
Coyle claimed at first sight he felt it was just a full-blooded challenge between the two players.
But Holden came off worst and as Bolton players called for immediate assistance, referee Andre Marriner decided the tackle warranted Evans' expulsion.
"Stuart has gone to hospital,'' Coyle said. "I think the players reacted the way they did because a cut opened up on his knee.
"We hope it is nothing worse than that and there is no break or ligament damage but we will only know when we get the results back from the hospital.''
Holden wrote on his Twitter account: "Thanks for all the messages of support, will keep everyone updated when I find out the extent of injury."
Sir Alex Ferguson had no complaints over the red card, which will rule Evans out of Premier League encounters with West Ham and Fulham, plus the FA Cup semi-final against Manchester City at Wembley on April 16. However, he insisted Evans is not a malicious player.
"The referee has seen the player had a bad injury,'' said Ferguson, who watched the contest from the directors' box as he began a five-match touchline ban. "Both players went for the same ball, with their feet raised, and Jonny caught the lad. Once you raise your feet you are putting yourself in a dangerous area. It was unfortunate but we cannot complain.''
As it turned out, even though Michael Carrick had to operate as a central defender, Coyle felt the loss of Holden affected Bolton more than United going down to ten men.
"We have had five massive games in the last couple of weeks,'' Ferguson said. "It has been a hard programme and the lads deserve a lot of praise for that. This was not a 100% top performance from us but we never gave in.
"That is what the character of this club is all about. No other club in the country has got that. We are fantastic at gritting our teeth and getting something out of a dead situation.''
Ferguson confirmed he had lost Wes Brown to injury at half-time, a problem that, given the introduction of Fabio at right back, required Berbatov's arrival too to combat Bolton's added height.
"We have two weeks now to try and patch up the injuries,'' Ferguson said. "That is the biggest break we have. We should have Nemanja Vidic back for the West Ham game and also Darren Fletcher. I would love to have been able to bring Park Ji-sung on today too.''