The Dutchman pressurised defender Martin Skrtel into scoring an own goal before adding another himself in Sunday's 2-0 win over Liverpool.
That result helped take some of the pressure off under-fire McClaren but with United still in the Premier League relegation zone, he has work to do if he is to have any chance of keeping his job.
Wijnaldum is convinced the former England boss remains the right man to take the club forward, though, and has urged the board to stick by him.
"For this club, he is the best we can get right now. I hope the club will give him the faith and keep him here," Wijnaldum told the Daily Star.
"That's the thing in football. When results go wrong, everyone says the trainer is responsible for that. It's not fair every time.
"I didn't know there was talk about his future but against Liverpool, we fought hard both for him and the team."
The win over Liverpool followed a 3-0 home defeat to Leicester and a 5-1 drubbing at Crystal Palace and Wijnaldum revealed there had been frank discussions among the players in the wake of the Selhurst Park loss.
"If you want to go further and climb the table, you have to be honest with each other," he added.
"Sometimes, it can be hard to be honest but it had to be done."