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The South African defender rescued a point for Derek McInnes on his return to Gorgie, but he was left frustrated after watching Rangers surrender their first-half advantage.
Kevin Kelsy had fired the visitors ahead and they looked on course for victory before Hearts turned the contest on its head after the break. Claudio Braga hauled the hosts level before Calvin Miller completed the comeback, leaving Rangers staring at defeat.
But Makhanya came to the rescue in the closing stages, powering home a header to earn a share of the spoils and deny Hearts a memorable win.
Despite his late heroics, the centre-back admitted Rangers fell well short of the standards expected of them and claimed Hearts simply showed more desire when it mattered most.
Speaking to Sky Sports, he said: "Honestly, I think it's a very disappointing game. We showed good character to come back, but overall I think we're a much better team than what we showed tonight. We'll take the point and move forward.
"I just feel we lacked character in the second half. We needed to start the half the right way, but we came out a bit sluggish. It's a game we need to move on from as quickly as possible and focus on the next one.
"Maybe Hearts showed more desire than us. I felt they were outworking us at times and that's why I think there was a lack of character. It's something we need to fix as a team.
"I think we made the game difficult for ourselves. Hearts fed off our mistakes and we put ourselves under pressure. We were losing balls we shouldn't have been losing and weren't able to control the game. We just made things harder for ourselves than they needed to be."
Tig