Moyes: Mirallas needs to toughen up at Everton
Moyes is not sure the flamboyant Belgian international, who has scored in three of the last four league games, can combine the necessary level of toughness to his natural pace and ability.
The 25-year-old has suffered a series of minor injuries which have occasionally prompted him to ask to be substituted during matches.
"He's had a lot of niggles. He's not quite adapted to what the Premier League means and how the games go," Moyes was quoted as saying by British media on Thursday.
"I look at him and he's signalling to me with 15 minutes to go - so maybe he's not quite got what's required at Everton or the Premier League.
"We're finding we're getting 60 or 70 minutes into games and thinking - Will he keep going? Will he pick up an injury? Will he lose concentration?," Moyes added.
"His ability is not in question but there are a lot of players who can take time to get used to the Premier League. What he has got in abundance though is pace, ability, he can score goals, he can take you on and he can play in two or three different positions."
Mirallas, who scored a superb individual goal against Stoke City two weeks ago, arrived at Everton from Olympiakos Piraeus in the close season and spent six weeks on the sidelines with a hamstring complaint early in the campaign.
"Maybe he's not quite got up to match speed all the time and we may have to deal with it to the end of the season," added Moyes.
Everton, who rarely shy away from the gritty physical battles of the league, are sixth in the table and have an outside chance of taking the fourth Champions League qualifying berth.
They host struggling Queens Park Rangers on Saturday.