“Steven Pienaar has a bit of an injury, so has Johnny Heitinga, so we had them to worry about,” said Moyes.
“I've got a few other problems. Leighton Baines has a bad ankle which we need to watch and be careful with.
“But we needed him. We have to respect the players at this level and what they offer.
“A lot of our players have probably played at this level and come on through.
“It's always hard in a game like this because the Premier League is always all consuming. But the players did a really good job and kept their focus right. Their application was spot on.”
Moyes, meanwhile, dismissed reports linking Victor Anichebe, one of several impressive performers for Everton last night, with an imminent move to Premier League rivals Reading.
“It’s not true, I'm not selling anybody,” he said. “Victor had a real go and had some creative moments as well.
“The fourth goal was a great goal and Ossie's was a terrific goal as well, then Victor laid on Felli's as well.”
Everton will discover their fourth round opponents next Tuesday when Sunderland and Bolton Wanderers replay after a 2-2 draw at the Reebok Stadium last weekend.
And while Moyes believes the draw has been unkind he has targeted a lengthy run in the competition.
“The draw makes the decision how far you can go,” said the Everton manager. “If you get cup draws it can help you, if you get bad draws it can make winning any cup competition hard, and I think we've got a tough draw in the next round whether we face Bolton or Sunderland.
“But we're only in one more cup competition. It's not as if we've got Europa League or Champions League football to contend with so hopefully we can cope with those extra games and hopefully there'll be a lot more extra games because we keep getting through.”