Owen was well below par in England's opening 2-1 defeat by France and his main contribution to Thursday's 3-0 win over Switzerland was to set up the first of Rooney's two goals.
"I think Michael would be disappointed that he's not scored a goal and probably not played as well as he would have liked," McClaren told a news conference on Sunday.
"But Michael's world class. He gains the respect of every defender he plays against and he will score goals. We're very very hopeful. I think there was an improvement in the last game."
However, if the drought continued in Monday's decisive final Group B game against Croatia, McClaren made it clear Owen would be expected to help his 18-year-old strike partner.
"If he's not scoring, then he's got to do as he did in the Switzerland game, set up the first goal and create room for the likes of other people like Wayne Rooney," he said.
McClaren, who ruled out dropping Owen, had nothing but praise for Rooney, now the youngest scorer at a European championship.
"Wayne Rooney has been a revelation in the two games and he's an absolute coach's delight to work with -- he does nothing but want to play football."
"His temperament's fantastic, nothing fazes him, he's got no fear."
Though a point on Monday would put them into the quarter-finals, McClaren said England were not underestimating a Croatia side who drew 2-2 with France.
"There's no complacency in the camp at all," he said. "Anyone who can give France a game and draw deserves the respect of everybody and they'll certainly get that from us.
"They're a very good team technically, very quick, a good counter-attacking team."
Ruling out a tactical game plan from manager Sven-Goran Eriksson, McClaren drew a parallel with England's passage to the second round of the 2002 World Cup.
"We were in a similar position two years ago in Japan when we needed a draw against Nigeria. It was a difficult game but we got through," he said of the 0-0 stalemate.
"We approached that game aiming to win it and it'll be the same tomorrow against Croatia."
