McClaren is already without forward Wayne Rooney with an ankle injury and the absence of Owen will leave him short of options up front.
Speaking immediately after the match, McClaren said: "It was a strange one, it was Michael's standing foot.
"He's pulled his thigh and unfortunately he's out."
BBC Sport understands Owen could be out of action for more than a month with his latest injury setback.
Liverpool striker Peter Crouch scored the winner in the victory over Austria and would be the most likely to lead the attack.
Jermain Defoe could come into the reckoning or McClaren may opt to play five in midfield with either Steven Gerrard and Frank Lampard in a more advanced role.
"I do believe we do need to win against Croatia but we go into that game without two centre-halves and two strikers we would pick," added McClaren.
The problems at centre-back see John Terry out with a knee injury while Rio Ferdinand is suspended.
"It's disappointing but I believe and hope that Wednesday will be important.
"I believe there's enough in that dressing room and the squad has enough spirit that we will do it."
But McClaren was buoyed by the performance of Sol Campbell and Joleon Lescott in central defence in Austria as well as the display of Micah Richards when he moved into the middle from right-back.
"In the first half, we got quite a lot out of it," said McClaren. "It was good but we could have scored more.
"The second half disappointed me in some ways. I expected us to go on the attack and get more goals but we were disappointing in the second half.
"But there were plusses. Scott (Carson) kept a clean sheet, Joleon and Sol were formidable and Frank, on his return to the team, was man of the match and rightly so."
