The draw meant Arsenal slipped to fourth after failing to win for a third league game, but Spaniard Bellerin said there were plenty of others that could follow his path from academy to first team and keep up the pursuit of leaders Manchester City.
"I have said it before, there is great depth in the team. There are a lot of young players in the team waiting to come through, and we have a lot of quality training with us every day," Bellerin told the club's website.
"They are ready to step up so obviously every single player on the bench can do the same job as every single player in the starting eleven. We don't need to worry about (the injuries).
"The only thing we need to do is go out onto the pitch with the right mentality, it does not matter who we play.
"We need to look at ourselves and realise that this is not the way. We need to push ourselves a bit more and play better football if we want to be at the top," the 20-year-old added.
"What happened on the pitch (against Norwich) was not a great experience but we need to try and bounce back so we are ready for the next game."
Arsenal host fourth-from-bottom Sunderland in the league on Saturday.
Arsenal injuries
Santi Cazorla - Knee problem
Laurent Koscielny - Hip problem
Alexis Sanchez - Hamstring
Mikel Arteta - Calf problem
Francis Coquelin - Knee ligament
Theo Walcott - Calf
Danny Welbeck - Knee
Jack Wilshere - Ankle
Tomas Rosicky - Knee
Kieran Gibbs - Calf
(Reporting by Shravanth Vijayakumar in Bengaluru. Editing by Patrick Johnston)
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