Matsatsantsa have only won twice in 12 matches since they lost the Confederation Cup decider to Congolese giants TP Mazembe in November last year.
Tinkler's side have consequently slumped to 11th on the Premiership table with 21 points from 17 fixtures - just five points above the drop zone, although they have a game in hand on every team except for fellow strugglers AmaZulu.
Sundowns also saw their domestic form take a knock after winning the 2016 Champions League, as did 1995 continental champions Pirates after reaching the finals of the top-tier event in 2013 and the Confed Cup two years later.
"Like I said, I think there is no team that has gone to a CAF final that hasn't felt this," said Tinkler, who guided Bucs to the Confed Cup final in 2015 when they lost to Tunisian powerhouse Etoile du Sahel. He also assisted Roger de Sa during Bucs' narrow miss at a second star.
"I think you saw it with Sundowns, you saw it with Pirates. I experienced it with Pirates you know. I don't think people actually understand how difficult it is. And it is more emotional for the players than anything else. I don't think it's a physical issue, I think it's more of an emotional issue because to get to a CAF final was a very long road.
"We got to a Nedbank final, we got to a CAF final, we got to an MTN8 final, and that takes a lot of hard work and the players have to go through a lot of pressure.
"Normally what you would find, your season would end, be it a Champions League final or a Europa final, whether you won or lost you get at least five weeks to recover, regenerate and get away from the game before you start your pre-season and get back to work.
"That's not the case here. We got to get back here and catch up on league fixtures. What happend to us is you got to sit and play 10 league fixtues in the space of 30 days, and we expect these guys to bounce back every three days and put on the same performance, the same energy, the same level of concentration... that's not easy, that's extremely difficult," concluded the SuperSport coach.
United next host relegation-threatened league champions Bidvest Wits at Lucas Moripe Stadium on Saturday night (20h15). Tinkler will be without suspended centre-back Morgan Gould.