"Everyone is working together," said Parry.
"Everything was relatively calm during the close season compared to the publicity at other clubs and now we just want to focus on winning games.
"There is a dialogue between the two owners on a regular basis. And they have been supportive throughout the last six months, especially in the transfer market.
"People forget that we have bought Robbie Keane and paid a huge fee for Javier Mascherano. So the commitment has still been there. They have been supportive through this transfer window and, at the moment, it is stable."
Parry also insists he has no plans to quit his role at Liverpool despite being linked with replacing Brian Barwick as chief executive of the Football Association.
"I'm still here but it's not about me. The story should always be the players," he said.