While the Reds avoided the major teams in the draw, Parry is aware that the trio of opponents awaiting will offer a firm challenge to Rafael Benitez's side.
Parry said: "We will give all of the teams respect but we won't fear them.
"We are delighted to be back in the competition and we know there are no easy games at this stage. We may have avoided the biggest teams but that doesn't necessarily mean we've avoided the best, as last season proved. We've also avoided the really lengthy trips which is good.
"Rafa will know a lot about Deportivo, Monaco didn't do too badly in the competition last season and we know about Olympiakos having been there before."
