The Scot has come under fire for his start in charge of the Premier League champions, who currently sit 12th in the table after six games following a 2-1 defeat to West Bromwich Albion at Old Trafford on Saturday.
Moyes's side travel to Shakhtar in the Champions League on Wednesday, and his opposite number has told the media that he needs to be given a chance.
"I have watched most of United's recent matches and can say that David Moyes hasn't found his best lineup yet, as he is changing four or five players from game to game," Lucescu said in his press conference. "The link-up play between their players is not as good as it used to be so the team suffers, which is happening with us too because Shakhtar have a lot of new players.
"I know about Moyes's work at Everton – he is clearly one of the best coaches in the Premier League, but he needs time to organise his new team properly. I think Carlo Ancelotti, Manuel Pellegrini and Jose Mourinho are having the same difficulties. I am sure that sooner or later he will resolve all his present problems, but I hope it will happen after the game in Donetsk."
Shakhtar Donetsk host United at the Donbass Arena tonight with kickoff at 7.45pm.