Henri Anier slotted home the opener after 40 seconds but Aberdeen almost hit back immediately with Peter Pawlett and Calvin Zola both hitting the bar inside the first half hour.
The Dons had to wait until just after the hour mark to level through Niall McGinn when Stephen McManus conceded a penalty following Stevie Hammell's heavy touch.
But they went from strength to strength and Mark Reynolds 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 and McInnes realises there will be a wave of optimism from the Aberdeen support, who brought 1,879 to Fir Park.
But McInnes cautioned: "Performances like today will give the support every encouragement, but it's two games. It's nothing more than a good start. We face another challenge in Celtic.
"The fans gave been here before so I don't think anyone is getting too excited."
McInnes also admitted it was the ideal time to play Motherwell following their Europa League exit against Kuban Krasnodar in Russia on Thursday night.
And Motherwell manager Stuart McCall felt his side would need to maintain their good start for longer.
"I don't want to make any excuse but I know what it was like last season against St Mirren (following a Europa League game at Levante) when we were hanging on with 20 minutes to go," McCall said.
"I thought, to get anything out the game, we needed to be going into the last 20 minutes ahead.
"It's only natural, you get back in your bed at seven o'clock in the morning after the flight. 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."
But McCall, who revealed referee John Beaton had penalised McManus for a pull for the second penalty, added: "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."