The 31-year-old midfielder completed a free transfer to the Hammers, where he started his career, on Friday after two-and-a-half years at Anfield.
"The best move for all parties," Rodgers said at his press briefing today.
"Joe's a good guy who I've known for a long time. It has been difficult for him here across his time. In the short period I've been here, he's never been a problem for a minute - he's a good man.
"But for both, it was best. Joe needs to play; he's going back to his home - it's where he grew up and he knows and loves the club. We thank him for his efforts and both parties move on."