Allen, who became a Liverpool player on Friday, looked on from the stands as the Reds' preseason programe drew to a close with a 3-1 victory over Sami Hyypia's Bayer Leverkusen on Sunday.
And Bellamy, who starred alongside the 22-year-old for Team GB at this summer's Olympic Games in London, is convinced Liverpool's latest recruit will thrive under new manager Rodgers at Anfield.
"I spent the last three weeks hounding Joe Allen to go to Liverpool," admitted Bellamy. "They have got an immense player.
"Joe, Brendan and Liverpool will all be great winners out of this. It has been a pleasure to spend the last few weeks with him."
When Allen arrived on Merseyside at the end of last week, Bellamy was on his way out of Melwood and heading in the opposite direction to complete a switch to Cardiff City after a second year-long stint at Anfield.
And Bellamy, who scored 11 times in 36 appearances during the 2010-11 campaign, admitted leaving the club he supported as a child proved highly emotional and he thanked the Reds fans for supporting his decision to return to Wales.
"The hardest thing for me was leaving Liverpool," said the 33-year-old. "I am a Liverpool fan.
"I'm also a huge fan of Brendan and I think Liverpool will do great under him. But even that couldn't tempt me. It just wasn't going to happen for me.
"The supporters at Liverpool have been immense and the way they have been with me about this has been amazing. But my mind was made up. I am doing it for the right reasons."
Photo via Liverpoolfc.com