Pirates returned home yesterday after losing 2-1 on aggregate to Tunisian side Etoile du Sahel in the Confederation Cup Final in Sousse on Sunday night.
"We were all disappointed, every single player, waking up the following morning and realising that we still going to stay another 48 hours in Tunisia," says Tinkler, who is set to discuss his future with Bucs management this week.
"It was not an easy thing and the mood was down. In the afternoon I felt we needed to get out of the rooms. We went to the beach to play head tennis and it helped a little bit and the mood started to improve.
"We set our target to win this tournament. I felt what we done well, particularly in the second half, where we showed we deserve it more than what they did."
Tinkler says the squad has been given a few days off to recharge their batteries.
"It is important now having a break, giving the guys a couple of days off. We are gonna come back and start working ahead of the game against Sundowns. The good thing is we got close to three weeks to prepare for the Sundowns game.
"The guys who didn't go to Tunisia, they will also need to step up and help the boys that have gone throughout the whole competition. Remember we have been playing two seasons non-stop. Obviously emotionally and psychologically it does affect you a little bit. We have to find a way and we have to bounce back."
The Buccaneers are 11th on the Absa Premiership table with 11 points from nine games - 12 points shy of second-placed Downs, who have played two extra matches.