Allardyce has never seen eye-to-eye with Benitez when in charge of both Rovers and Bolton Wanderers.
"I've no worries about what he thinks about me or my team," said Allardyce. "My side can beat them on any given date - that is the most important thing to me.
"We know we can beat them because I did it at the Reebok. Because he didn't like it, he found some excuse about how we played. Arsene Wenger did it, Jose Mourinho did it - they all do it when they get their backsides smacked about.
"He has had a bee in his bonnet for a while. He is entitled to have his opinion as everyone and it's nice to have someone complaining about you when you are beating them. What's the point of having a drink after the game and the other manager saying 'don't my team play good football' when we've been beaten 2-1 or 3-1.
"I know how good a boss I am and how good a job I can do. I wouldn't have been in the Premier League for 19 years if I couldn't do it.
"So it's not of any importance to me what Rafa Benitez thinks about what I do and don't do."