Matsatsantsa were thumped 4-1 at home by Bidvest Wits in Atteridgeville on Saturday, leaving the Tshwane giants four points above the Premiership drop zone with 21 points from 18 games.
SuperSport have battled since losing the CAF Confederation Cup final to TP Mazembe in November last year, only winning twice in 13 outings.
However, Tinkler believes in his ability to turn things around for the MTN8 and Nedbank Cup holders.
"I am a person that has belief in my ability," said Tinkler, who replaced Stuart Baxter at the club in the off-season after impressing at the helm of Cape Town City in 2016/17. "I am a hard worker. I have never given up in any challenges in my life and I am not intending to start now.
"That's the message that I need to transmit to the players. They must understand that we need to win those matches. We need to get out of this situation. Nobody is gonna help ourselves. We got to help ourselves and the only way to do that is by lifting yourself and motivating yourself to come and perform in the next game. In every game it's gonna be a fight. It must be a fight for 90 minutes and not 45 minutes."
Some fans on the weekend voiced their displeasure at Lucas Moripe Stadium, and the ex-Orlando Pirates mentor says he understands their frustration.
"It's normal, I feel the same way. They must understand we also feel as bad. We are professionals, we don't like losing. I am a coach that doesn't like losing. I hate losing but it's part and parcel of the game. I don't blame them for the way they are feeling."
United next host AmaZulu at the same venue on Wednesday (19h30).