Robinho, who arrived in the summer from Real Madrid, has been told that a police investigation against him has been completed with no charges to answer.
Dunne told City's website: "It was an awful thing to be accused of and it would affect any man in that situation. He's got a young family and they are his main concern so hopefully that has lifted a bit of weight off his shoulders and he can start playing with a smile on his face again and showing what he can do."
Robi's form has come under scrutiny time and again as City battle for a seventh-place finish in the Premier League and a place in the semi-finals of the UEFA Cup by beating Hamburg, their first-leg rivals on Thursday.
Dunne added: " All the criticism doesn't help him. It's easy for people outside the club because nobody seems to want him to do well. So it's important for us here and the fans to be 100 per cent behind him.
"Every stadium we got to, people are expecting him to do amazing things. It's not going to happen all the time. He's probably feeling the pressure of having to keep proving himself. Once he relaxes he will be fine.
"The players see how good he is every day in training. We all firmly believe in him and that he will return to his earlier form. That will be a real boost for us."