Tinkler was appointed caretaker coach on Friday following the resignation of Roger de Sa, who cited personal reasons for leaving the position he held since September 2012.
“I called the technical team in to explain what had happened and we discussed that we needed to get the team to support us,” Tinkler said after the game at the Orlando Stadium.
“The boys showed great character in the second half. We had a tough week with the coach leaving but the boys responded superbly.”
Sibusiso Vilakazi opened the scoring for the visiting Clever Boys on 20 minutes, but saw the lead disappear shortly after the half-time break, thanks to Helder Pelembe’s first goal as a Buccaneer 10 minutes after the interval.
Kermit Erasmus then came on from the bench and grabbed Pirates’ second, as the Sowetans completed their comeback and handed the team three valuable points.
“I expect the players to give their all because if they do that, then I can’t point fingers at them if we have a poor result,” Tinkler said.
“I didn’t think about the Wits game in any context other than it being another three points on offer.
“Pelembe holds the ball up very well and needed someone that can play close to him to feed of that. Kermit does that very well.”
Tinkler made an emotional plea to supporters and staff alike, insisting that the Sea Robbers were not yet out of the title race and stood a good chance of challenging for Premiership honours.
“We have quality in our side. The guys just need to believe in themselves,” he said.
“I’m proud to be at this club, the biggest in the country in my opinion. We need to remember that when we approach our games.”
The win was enough to see Pirates move up to sixth place in the Premiership standings, as they continue to play catch-up in the league, following their Caf Champions League commitments late last year.
The former Bafana Bafana international and assistant to De Sa emphasised the need for Pirates to win their remaining home games of the season, in order to make the Orlando Stadium a formidable venue for the rest of the league.
“It’s something that I want to focus on. Teams need to come here and respect where they are. We need to build that fortress.
“All the games we have lost have been at home. I spoke to the players about that. This is our castle and we have to defend that.”
Meanwhile, Wits coach Gavin Hunt was left frustrated after taking the lead before relinquishing it to the home side, revealing that the Clever Boys were slightly undercooked heading into the new year.
“What do you expect when we haven’t played for seven or so weeks, and they’ve played three or four games?” Hunt said.
Wits last played on December 21, while Pirates had taken part in four games and had been well-prepared by the time they met Hunt’s troops.
“We were always going to be rusty, if you don’t have that match intensity, you’re going to struggle.”