Chelsea were in full control when Jonny Evans' first-half own goal was followed by goals from Juan Mata and David Luiz shortly after the break.
But United were handed a lifeline by referee Howard Webb as he awarded a pair of debatable penalties, which Rooney converted before substitute Javier Hernandez headed in a late equaliser.
Despite the comeback, however, Rooney was disappointed to lose ground on Manchester City in the title race.
"It's two points lost," Rooney told Sky Sports 1.
"We understand that, but after being 3-0 down - the City players at home must have liked that - we enjoyed the way we fought back.
"A lot of teams might have put their heads down and accepted defeat, but we never put our heads down."
Rooney claimed he did not see the penalties, but was confident of converting both.
"The two (penalties) we got I'm not sure. Thankfully the referee gave them," he said.
"I was always confident. I waited for the keeper to make his move and put it the other way."