Phil Jagielka is a major doubt for next Saturday's FA Cup quarter-final after sustaining a serious gash to his ankle against Reading.
Stand-in skipper Jagielka had to be substituted just four minutes in to Everton's 3-1 win over the Royals and will now undergo surgery to repair the damage.
Moyes was frustrated with the tackle by Reading forward Adam Le Fondre and says he expects it to cost him the England defender’s services for at least a fortnight.
"Jags is bad," he said. "He is going to get surgery on his ankle - not to repair the bone but to stitch it up. It's a bad, bad gash.
"I'm not [happy with the challenge]. I'm not happy with the challenge that we've had on our goalkeeper [Tim Howard] in the last game that puts him out, and then I'm not happy with the challenge today that puts Phil Jagielka out of the game.
"I don't mind robust challenges - I'm quite happy for a bit of that. But one that puts out arguably one of my best players [I'm not happy with that]."
Moyes admitted he is still waiting to learn the true severity of the injury but asked if the 30-year-old is likely to be available for the clash with Wigan, the Blues boss added: "[It will be] a couple of weeks maybe. Normally if you get a cut around the ankle it's that because it's an area where you kick the ball. It's not something [that heals quickly]. It's a real, real blow to us."
Moyes was also disappointed officials didn't respond when substitute John Heitinga appeared to be fouled by Noel Hunt.
He said: “I've not seen it [again] but I will have a look at it and see. I was surprised the referee didn't stop the play but if he didn't see it you might have hoped that one of his two officials might have possibly spotted it.”