"I felt a wee bit aggrieved with one or two decisions but they're always honest decisions," said McInnes.
"I'm not going to be too critical of a referee. I felt, at the very least, we deserved one penalty kick, which we managed to get."
Refereeing standards have been in the spotlight this season and the Scottish FA's head of referees Hugh Dallas admitted recently that it had been a poor campaign for officials.
"I think it's easy just to criticise referees and we've felt aggrieved a couple of times this season, more than a couple of times," said McInnes.
"The good thing from our point of view is that there's a man in charge, Hugh Dallas, who has got to be commended for trying to improve things.
"He knows he's got a lack of experience with top-flight referees and they have to make mistakes along the way. We just hope that eventually they come out of it and there's fewer mistakes made, especially the bigger ones.
"I'm disappointed with one or two things today but I don't think you go through many games with not too many complaints about a referee and I think they are working hard."
Meanwhile, McInnes was delighted with the response from his team against Hibs after falling a goal down to Anthony Stokes' third-minute penalty.
There was a minute's applause before kick-off in memory late Hibs stars Alan Gordon and Bobby Smith on the day that the Easter Road stadium's East Stand was closed ahead of its reconstruction.
"We didn't start the game properly with a wee lapse in concentration," said McInnes.
"We made the players aware that Hibs would come out on the front foot. We felt that they would come out and try to show their colours and show their reaction to losing heavily (against St Johnstone earlier in the month).
"There was a lot on today emotionally for Hibs and we felt that from the crowd but I thought we silenced them for long periods because of how we approached the game.
"Once we went behind, I thought we then started to show composure. We played the game in their half for the majority of the game.
My own target, and the players are well aware of it, is to make sure that we're an SPL club this time next year
Derek McInnes
"I thought the least we deserved was a point. They kept knocking at the door. We got the right decision in the end and Liam Craig has tucked it away and I'm delighted with the players' reaction throughout.
"My players never ever give up the ghost. They keep going and keep working hard and they got their reward with the goal towards the end."
The result keeps Saints in contention for a top six place, sitting nine points behind sixth-placed Hearts with three games in hand.
"I felt we could win points in this league, could go and compete, have a positive approach. I thought I had good players that would enjoy the SPL and that's been the case," added McInnes, who led St Johnstone to promotion last season.
"If where we are has exceeded it, I'm not too sure. My own target, and the players are well aware of it, is to make sure that we're an SPL club this time next year and then we could possibly raise the bar and that's still our aim.
"Whether that changes in the next month or so, only results will determine that.
"But if the players show the fight and the determination and good quality of play that they've shown on a regular basis this season and carry that real goal threat we've had from the off, then who knows?"
Source: BBC Sport
Source: BBC Sport