News emerged yesterday that the Mpumalanga-based side dismissed the former Acornbush United and Baroka FC coach due to poor results.
But according to Thobela, Makhubedu asked to be allowed to step down as he could no longer handle the pressure of coaching the team.
Makhubedu is still with the club and has travelled with the squad to Cape Town for their GladAfrica Championship match against league leaders Ajax Cape Town on Wednesday (15h30).
"I don't think Makhubedu had any problems, it's just that he felt he was under pressure," Thobela clarifies to snl24.com/kickoff.
"I don't think I'm under pressure to appoint a new coach. Not at all. He is the one who requested that he wants to be released from his duties but even now as I'm speaking I'm travelling with him so there's no bad blood... we are traveling with him to Cape Town.
"He's still with the team even now as I'm speaking. But obviously he will not be sitting on the bench because he has made his decision, so we just have to respect his decision, that's all. He is going to watch the game like any other person."
Makhubedu only managed four wins, five draws and lost six times in the 15 matches he was in charge.
Thobela is in no rush to find a replacement for Makhubedu and has left the team in the hands of goalkeeper coach Innocent Nkhwashu.
"No man I haven't decided yet. I told myself to first have a look at the Ajax game then I will decide after [if we need to appoint a new coach now].
"We are not under any pressure to appoint a coach immediately. Our goalkeeper coach Innocent Nkhwashu will take over."