Uefa president Michel Platini had laid out a proposal which would mean future FA Cup winners would take the Premier League's fourth Champions League spot.
And now Parry has declared that all of the Premier League clubs at the conference rejected the idea. "Liverpool, Manchester United, Chelsea, Arsenal and Newcastle all feel the same way," he revealed on Liverpool's official website.
"It's not a question of self-interest by the big clubs.
"It's just more of a lottery in the cup.
"There is a strong feeling the Champions League place should be based on Premier League performance."
Parry also revealed that the Premier League is supporting the English clubs' stance on the matter.