Elmander required five stitches in a head wound and Coyle was clearly not impressed by the challenge, which went completely unpunished by referee Martin Atkinson.
"I can only assume the referee has not seen it," said Coyle.
"Vidic has caught him with an elbow. There was blood pouring out of it.
"I am not looking for excuses but anyone who has seen it knows it was a terrible challenge."
After branding the FA's disciplinary system "dysfunctional" last week after Steven Gerrard was not punished for two incidents, United boss Sir Alex Ferguson will wait to see what action, if any, is taken against the Serb.
Key will be Atkinson's observations because if the referee claims he got a clear view, as was the case with both Gerrard incidents, the FA are powerless to act.
"It was a real battle," admitted 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."
The possibility of Vidic being suspended for next weekend's crunch Old Trafford encounter with Chelsea will cast a pall over United's preparations for their Champions League quarter-final with Bayern Munich on Tuesday.
There is some good news for United though, with Ferguson confirming both Wayne Rooney and Rio Ferdinand will be fit to face the Germans after missing out against Wanderers with a bruised heel and a groin injury respectively.
"They were just a bit tender," said the United boss.
"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."
The calculated gamble paid off as Dimitar Berbatov scored twice and Darron Gibson added another with his first touch to round off a comfortable win.
However, United were indebted to Jlloyd Samuel, who inexplicably drove Ryan Giggs' low cross into his own net seven minutes before the break, the 11th own goal the Red Devils have profited from this season.
"Jlloyd cannot feel any worse," reflected Coyle.
"Next time he may make a better decision. It was a nice ball in from Ryan Giggs but no more than that."
For United it was the perfect response to the seven goals Chelsea scored against Aston Villa earlier in the day, and sets up a mouthwatering clash next week, whether Vidic is available or not.
"Chelsea scoring seven did not put any more pressure on but when you see that turnaround in goal difference in four days (11) it is a challenge.
"But if you put the gauntlet down, Manchester United will always accept it."
Barclays Prem 2009/10 Win Outright: Man Utd 4/5