Italy now await them in the quarter-finals on Sunday, and Moyes is a fan of the way England have played to their strengths.
"You have to play to win and that is what England and Roy have done," said the Everton boss. "Whatever you say, England have been in tournaments [before] and not had much success, but [this time] they have had a few games, won a couple and drawn one.
"It may not have been attractive to some people but others have been talking about the Spanish who play thousands of passes a game but aren't entirely happy.
"England are playing a way that suits England at this present time," he added. "Will it take them far enough? I don't know, but at the moment I think they are doing a great job.
"I think Roy would like to [play more expansive football] but maybe at the moment doesn't have the players.
"But they do have Steven Gerrard and Scott Parker doing a good job and terrific centre-halves. Defensively they are very sound but it is just maybe in the forward areas England don't have the options some other teams have."