Steven Gerrard backs Rangers captain to bounce back from Europa League disappointment
The right-back endured a torrid night as Rangers let slip a half-time lead to go down 2-1 against Young Boys in Bern in the Europa League.
Tavernier lost possession deep in his own half before Young Boys levelled and then made a misjudged attempt to cut out a ball forward before the home team hit a stoppage-time winner.
But Gerrard believes his skipper will show his true colours.
"James is the captain of this team for a reason," the Rangers boss said. "He is maturing, he is big enough to handle the criticism that comes his way.
"That's one thing you are looking for in your captain. Football is not just about highs and praise and everyone telling you how great you are. It's about recovering from setbacks, being able to handle the tough times as well as the good times.
"Look, we are all responsible for that result. Of course there were a couple of mistakes that have affected the result but we are all in it together.
"He has been absolutely fantastic for me, he has been fantastic for his team-mates and the supporters, he has provided some incredible moments and some fantastic performances. So we have to remember that as well."
Gerrard is counting the cost of the encounter in other ways with Ryan Jack out of Sunday's Ladbrokes Premiership visit of Hamilton and defender Filip Helander a doubt with a foot knock.
The Gers boss has other injury worries after the game on an artificial surface but wants to keep changes to a minimum.
"It was a tough game on a tough pitch," he said. "We have a couple of dead legs and a couple of people with tight muscle injuries so that could affect team selection but I want to make as few changes as possible. I want to keep the rhythm going in terms of our level of performance."
Jack is a doubt for Scotland duty and Rangers are awaiting the results of a scan on his leg injury.
And Gerrard admits any extended absence would be a huge blow, although he is hopeful over the prognosis.
"Ryan sets the standards every single day in training," Gerrard said. "More often than not he is the strongest trainer. He's a winner.
"We are absolutely delighted with him. We have made him a contract offer that we are hoping will progress and will get signed very soon, and we have our fingers crossed for this scan because he is very, very important for me."
Joe Aribo could return after missing two games with a head wound, but only if a specially-made mask proves comfortable enough to wear in the game.