His side moved ahead of Rangers thanks to a hard-fought 2-0 victory over Partick Thistle at Pittodrie on Saturday.
Goals from substitutes Jayden Stockley and Ryan Christie earned the points for the Dons, and McInnes admits his side are in a battle to secure the runners-up spot.
He said “We recognise we’re in a fight. There’s still a lot of football to play, but the league table is probably what we thought it would be like. Celtic were going to be ahead of others if they played to their potential.
“There’s no real surprises. We always felt we were going to be competitive, and as long as we’re there in 15 games time, that’s all I’m concerned about.
“A lot of our players are playing, individually, well, but I’m fortunate I’ve got different players available to suit what’s needed.”
Aberdeen were unchanged for the seventh consecutive game – despite having lost 1-0 at Celtic in midweek – and that consistency has been the key to an upturn in fortunes for the Dons. “We’ve a settled team, but it’s important to stress the ability and capability of the rest of the squad because they’re team players but they’re itching to play their part,” McInnes said.
Partick Thistle made four changes to the side who were defeated 1-0 at home by St Johnstone midweek, and assistant manager Scott Paterson is backing striker Ade Azeez to get on the goal trail despite the hitman passing up a golden opportunity to earn his side a point.
Five minutes after Stockley opened the scoring with a header, Danny Devine’s ball out of defence was bizarrely left by Andrew Considine, with Azeez lurking behind him. The striker looked for all the world like he had to score but, with only Joe Lewis to beat, he struck the outside of a post.
Paterson said: “If he’d scored, the game would open up even more and it might have played into our hands, but we can’t get to the end of the season and look at the chances we’ve not taken.
“Ade will keep going. He’s a striker, and they’re judged on goals. He’s just got to keep going, stay confident. He works very hard in training and defences are scared of him because of his pace and power. It’s up to him to take his chances.”
Azeez had another chance a minute from the end, but he blasted wildly into the crowd.