Viruses may still be infective if captured by the mask, but they're much less likely to infect you. If they're captured by an intermediate layer of the mask, they pose no threat. Even on the surface of the mask, the chance of you being infected by a virus particle that you touch on the surface of a mask when you take it off are overwhelmingly less likely to infect you than virus particles that you breathe in. Of course, when removing a mask, you should sanitize your hands afterwards, which nearly eliminates the risk from virus particles you may have picked up by touching your mask.
You should not pull your mask below your nose. If you do however, the chance of a virus particle coming off the mask and then going into your nose is dramatically less than if you had been breathing in these particles directly.