There are worries that Liverpool's squad is now too thin to successfully manage the hectic programme over the coming months, particularly given the early start forced upon them this year by the early rounds of the Champions League.
But Parry added: "Rafa is philosophical about the situation. He insisted we didn't pay for players who weren't worth the money.
"He is sure we are better placed to challenge for the top places this season. We want to push on from last season and we are still confident we have the players to do it.
"Have we got a better squad to do well in all competitions this season? Rafa's answer to this is yes."
Chile international Mark Gonzalez, meanwhile, will move to Anfield on loan from Albacete as soon as he can get a work permit, according to the Spanish club.
Gonzalez's proposed switch collapsed when he was refused a work permit because Chile are ranked outside the top 70 nations by FIFA.