Henri Anier scored after 40 seconds but Aberdeen almost hit back immediately with Peter Pawlett and Calvin Zola both striking the bar inside the first half-hour.
The Dons had to wait until the second half to level through Niall McGinn but Mark Reynolds soon headed them in front, before McGinn converted a second spot-kick to give them their first league win over Motherwell since November 2008.
McInnes said: "It wasn't the start we wanted but I thought it was a foul leading up to their goal; a Motherwell player jumped right into Joe Shaughnessy.
"But I thought our response was excellent. Even at half-time, we could easily have felt sorry for ourselves, in the fact we passed up a couple of opportunities and hit the bar twice.
"They got their just rewards. It was a good strong performance with the right level of mentality.
"They don't need to show me we have good players, I know I have good players, it's the other side we will need to show.
"We will need to come from behind again and at no point did I feel we were ever going to give up the ghost. It was an immediate response and there was some real good play in the first half."
The Dons now host Celtic with six points on the board in the Scottish Premiership but McInnes attempted to temper the wave of optimism in the stands.
"Performances like today will give the support every encouragement, but it's two games," he added. "It's nothing more than a good start. We face another challenge in Celtic."
Motherwell manager Stuart McCall rued the breakthrough that McGinn made 17 minutes after the restart.
"I thought, to get anything out the game, we needed to be going into the last 20 minutes ahead," he said.
"If you're still in there you can dog it out, but when you lose two goals like that, you could see the lift they got and we looked a bit leg-weary.
"The better team won. You can't afford to gift teams goals, especially good teams like Aberdeen who have threats all over the park.
"Having said that, the third goal, if that's a penalty then there's six or seven penalties in a game. But that's not why we lost. We conceded two poor goals in quick succession."