The current Chelsea manager replaced Mancini at Inter in 2008 and led the Italian side to two Italian league titles, the Italian cup and the Champions League.
Speaking ahead of Chelsea's Champions League last-16 game against Mancini's Galatasaray, Mourinho said there was no doubt who was responsible for Inter's success.
He said: "It's funny, it's funny. It's funny because my team in the final had Lucio, Thiago Motta, Diego Milito, Samuel Eto'o, Goran Pandev and Wesley Sneijder.
"From my 11 players, he didn't work with six of them.
"So he made a five-a-side team because I played with only five players from his team."
Mancini had earlier claimed: "Mourinho won the Champions League because he took a very good team.
"He took a team that, like Manchester City, I had built, a team that had a strong mentality.
"When I went to Inter, they played very bad football and we changed this."
Wednesday night's game will be special for Didier Drogba, who faces former club Chelsea and manager Mourinho.
Watch Chelsea take on Galatasaray live on Sky Sports on Wednesday. Coverage begins on Sky Sports 1 at 7pm.