Mancini last week said United could beat Swansea 10-0, and followed that up this week by re-iterating that the fixture is an "easy" game for the reigning champions as he seeks to take some of the pressure off his squad.
"He came here when we won the game 1-0 and we were clearly the better side and that was after Roberto spending about ?235million on a team," Rodgers said. "So I think he knows as well as anyone it won't be an easy game."
The two Manchester clubs are locked in a battle for the Barclays Premier League title, with City's 1-0 win over United at the Etihad Stadium putting them top on goal difference with two games remaining.
But Rodgers says the Italian has not paid the south Wales club the level of respect they deserve by repeating his attempted mind games.
Asked if he thought Mancini's comments were disrespectful, Rodgers said: "I think if you say it more than once it is.
"If you look at ourselves and the transition we have made from a Championship club into this level, the players have represented the club incredibly well in terms of the football we have played. Our analysis of our game, the preparation, the detail and commitment have been fantastic."
Rodgers also believes Mancini is wasting his time if he thinks his words have had any effect on Swansea and United's preparations for Sunday's meeting, pointing out how experienced Sir Alex Ferguson and his men have historically proved to be in these situations.
"He is maybe trying to affect one or two things but it won't affect us," he said. "We only worry about ourselves and I don't think there is anyway in the world you can affect a group of players with the experience of Manchester United, and a manager who is a multiple winner."
Meanwhile, 12th-placed Swansea can already plan for a second season in the Premier League after the point garnered in last weekend's remarkable 4-4 draw with Wolves secured safety.