Mancini senior led City to their first league title since 1968 last season but the former Italy international has found himself in the spotlight following his side's disappointing showings in Europe.
Big-spending City failed to get out of the Champions League group stages last term and look set for a similar fate this season as they lie bottom of Group D and five points adrift of second-placed Real Madrid with two games remaining.
Nevertheless, Andrea Mancini, who is currently on the books at Spanish side Real Valladolid having been released by City this summer, believes his father is doing a good job at the Etihad Stadium.
He said in Marca: "I don't understand the criticism. He's just become Premier League champion with City, which they haven't won for 44 years. I don't know what more he has to do."
Andrea Mancini was also asked about any similarities between Roberto and Madrid coach Jose Mourinho, who come face-to-face in the Champions League on Wednesday night.
The 20-year-old said: "They aren't alike. My father was a player for many years and you notice this. He has a lot of experience and knows more about football than Mou.
"Mourinho is more psychological, more of a motivator, he knows how to manage the minds of the players. The ideal coach would be a mixture of the two."