Giovanni van Bronckhorst insists he can steer the club through the current turbulence, despite not having spoken to the board about his future.
Rangers are seven points behind Celtic in the league.
The captain stated that dropping five points is not a crisis.
"I know I can turn it around or I wouldn't be here," he said.
Rangers were the worst team in the tournament with a minus 20 goal difference.
The injury-hit squad can regroup and make up ground in the league.
The manager said that winning was the most important thing. This allows you to play better when you win. We can improve with players coming back from injury.
Every day I talk to Ross Wilson. They haven't talked about my stance.
We need to add wins, but I didn't know if I had to do it or not. I didn't have that discussion with the board.
I know how it works. I have been playing football for a while. Everyone can see it for themselves. You don't want to let anyone down. I am a huge fan of Rangers and everything it embodies.
Winning games is my job. I don't understand why it's different for me if the manager isn't winning games.
The most important thing is to win tomorrow at home to Hearts, that is what I believe I can turn it around.
Tavernier said it would be "criminal" to write off title ambitions.
The full-back said that being clinical in front of goal was the most important detail. It isn't a crisis. I'm very confident in the team. It's one thing to say it on the field.
There are a lot of games left. It wouldn't make sense for us as a team to think that it's all over.
Results can change quickly and performances can change quickly as well.
Fashion Sakala has been added to the long injury list at Ibrox and will miss the game with Hearts and Saturday's visit to St Mirren with a muscle problem.
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