The teams played to a 1-1 draw in Atteridgeville on Saturday night.
Tinkler appeared content with his side's efforts against the Absa Premiership leaders and 2016 Champions League winners.
"There was a bus in defence and there was a Ferrari in attack," Tinkler said after the contest.
"He wasn't prepared for the Ferrari. You can't complain about the bus, but you must also be prepared for the Ferrari."
However, a visibly irritated Mosimane came back spitting fire and said he is ready to advise Tinkler on how to manage his club in handling CAF assignments.
Matsatsantsa's domestic form took a dive after they lost the Confederation Cup final to TP Mazembe in November last year.
"Which Ferrari? He has to come out of the relegation zone first to talk about the Ferrari. Where are the Ferraris? He parked the bus. What is he talking about?
"No. What Ferrari? He must manage his programme for Africa. I am waiting to advise him."
The result left Sundowns four points clear of closest rivals Orlando Pirates at the summit with eight games left, while SuperSport are five points above the drop zone in 12th place on the table.