A 2-1 defeat in Russia earlier this month has left the national team requiring a helping hand from Israel to qualify for next summer's finals.
But Rooney, who scored in Moscow, has offered his backing to McClaren and remains confident England can still reach the tournament in Austria and Switzerland.
"Before that Russia game everyone was saying how well the side was playing and how well the manager was doing," Rooney told The Sun.
"Of course everyone was really disappointed to lose, but one defeat doesn't make you a bad side or him a bad manager.
"These things happen - no-one's going to win every game. Steve's come in and done a great job.
"Everyone in the camp's really happy and the players really feel a sense of responsibility for what's happened.
"We're the ones playing the football, we're the ones representing the country and we feel responsible for it.
"Of course it would be a disaster if England don't make the Euro finals, but I am still confident we'll be there."