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," confirmed Coyle.
"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."
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," observed 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."