Defender Olwethu Makhanya claimed there was a “lack of character” in the team at the start of the second half after the South Africa defender headed an 89th-minute equaliser.

The centre-back claimed Hearts “showed more desire” and were “out-working” Rangers as they turned the William Hill Premiership game on its head.

“I got told about Makha’s comments,” McInnes said. “There was a period in the game where it looked as if we were second best. The running stats will tell you we weren’t, but I think it’s too easy to point fingers at character, and that’s a word that gets bandied about.

“We’ve got plenty of character. We’ve shown that already this season, with character to bounce back and get a result (on Wednesday) night when it looked as if we weren’t going to get that.

“The lads never give up. There’s a real determination and sheer will about them. But at times in the game, we have to acknowledge that we weren’t good enough, both technically and physically.

“I thought we were getting out-muscled at times and not getting to the break of the ball quick enough and a bit slow to anticipate, we were more reacting to things. I thought Hearts were on the front foot a wee bit more, ready to play the way the game was playing.

“Sometimes it can come across that way. We’re learning about these boys on the job, and the experiences will hopefully help us.”

McInnes will lead Rangers to Hampden for the first time on Saturday when they take on his former club Aberdeen in the Premier Sports Cup semi-finals.

Dons boss Stephen Robinson faced further criticism after a 1-0 home defeat by Falkirk left his side in the bottom four.

McInnes said: “The last round they beat Kilmarnock after extra time and penalties, they were down to 10 men. Robbo, really good management, he navigated Aberdeen to the semi-final, made good substitutions, set the team up and got through.

“He’s a good manager, Stevie. There’s no two ways about it. He has good experience.

“Yes, it’s not going brilliant from the minute at Aberdeen, but sometimes that’s just the way it is. We can’t get too focused on where Aberdeen’s at. We’ve got to focus on our performance.”