Vidic went unpunished but could face retrospective action - ahead of the key game against Chelsea - if the referee did not see the incident.
"Anyone who has seen it knows it was a terrible challenge," said Coyle.
"I am not looking for excuses but Vidic has caught him with an elbow and there was blood pouring out of it. I can only assume the referee has not seen it."
Victory over Coyle's side keeps United, for whom Dimitar Berbatov netted twice either side of a Jlloyd Samuel own goal and a late effort from Darron Gibson, a point clear of Chelsea at the top of the Premier League table.
However, Carlo Ancelotti's men visit Old Trafford on Saturday for a clash that could have a decisive influence on the outcome of the title race, and United can ill afford to be without Vidic, a key component of their back four.
Team was brilliant today... especially Vidic
Handsome and Modest
United manager Sir Alex Ferguson will therefore be hoping that referee Martin Atkinson saw the incident and includes it in his report, rendering the Football Association powerless to intervene.
Ferguson acknowledged the physical nature of the match and appeared unhappy about challenges on Patrice Evra and Nani by Bolton defender Sam Ricketts, confronting Atkinson at the break.
"It was a real battle," said Ferguson. "I said to the referee at half-time it was supposed to be a game of football. He handled it the best way he could.
"You need to show composure because the ball is never out of the air and we needed some fantastic defending at times.
"I don't know how many times Nemanja Vidic headed the ball clear but it must have been thousands."
United now travel to Germany for the first leg of their Champions League quarter-final with Bayern Munich, and Ferguson was relieved that his decision to rest Wayne Rooney and Ferdinand did not prevent United from seeing off Bolton.
Rooney is nursing a bruised foot, while Ferdinand is recovering from a groin problem.
"They were just a bit tender," added Ferguson. "Wayne has a bit of bruising in his foot. If he had played and got a whack on it he would have been doubtful for Tuesday.
"We have a big week. We have to use our squad in situations like this. I have no qualms about that at all.
"They have all done their job well and I will have Rooney and Ferdinand available for Tuesday."
Source: BBC Sport
Source: BBC Sport