The Glamour Boys suffered a 3-0 humiliation at the hands of 2019/20 season treble champions Mamelodi Sundowns in their first DStv Premiership match.
Khune was caught out of position for Kermit Erasmus' goal and also conceded a spot-kick when George Maluleka went over his challenge inside the penalty area.
"The way I see it, I think there were many errors from individuals, like technical errors you see," Mathebula tells snl24.com/kickoff.
"Because if you can take a lot a look at all the goals, there's a goal from a penalty which for me I feel was avoidable.
"Because if you can check even the player George [Maluleka, Sundowns midfielder] was looking for a penalty because he dragged his foot, it happens in football.
"But with the experience of Itumeleng Khune, well I believe he could have done better you know because he is one of the best. Ya so I think there were a lot of individual mistakes.
"And I don't think the players for now understand exactly what the coach wants from them. Because usually his teams don't concede much, they are very strong in defence."
There had been a feeling ahead of the match that pairing the two clubs so early in the season would possibly have been a mismatch after Sundowns' signing spree and Amakhosi's transfer ban.
"For me it's not an unfair competition," Mathebula says. "It's not like Chiefs don't have capable players, it's just that us as supporters we think for a team to compete they have to buy players.
"So for me, Chiefs have players with potential that coach Gavin [Hunt] will improve."