Cardiff completed the signing of 33-year-old striker Bellamy, who put pen to paper on a two-year deal on Friday.
"When Brendan got the Liverpool job he phoned me straight away on his first day," Bellamy told Cardiff's official website. "I felt honoured that he did that and he told me that he wanted me as part of his team.
"But my mind was made up. I wanted to come home. He gave me time to change my mind, but it wasn't going to happen.
"The fans have always appreciated me at Cardiff City and it was a pleasure to be here last time around. I feel people understand me here and it's great to be back.
"I'm not going to put pressure on myself and say we're going to do this or that, my intention is to go out and win every game I play in, it's as simple as that."