Newcastle coach Terry McDermott described Bellamy as "a little upstart" after Liverpool's 2-0 victory over his side in the Premiership last week.
"There was always going to be something from Newcastle but it doesn't bother me. Not at all," the Wales star was quoted as saying by BBC Sport.
"I was half expecting something because my being at Liverpool is hurting them.
"I'm sure there are people there (at Newcastle) who don't want me to succeed here, because it reminds them every time."
Bellamy was forced to leave Newcastle after falling out with former coach Graeme Souness.
He joined Scottish giants Celtic on loan before playing for Blackburn Rovers for two seasons.
"It was a ridiculously cheap fee I went to Blackburn for, it's not nice for me to be remembered for that," he said.
"What was it, about £3.75m? That hurts. I know that but that is the game we play."
Bellamy signed for Liverpool in the off-season and scored only once for Rafael Benitez's side so far.
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