Hodgson says he always believed Wayne Hennessey was innocent of making an offensive gesture during a club meal but felt the FA had a right to investigate.
"We always believed 100 per cent in his innocence, I have said that on several occasions, but I also understand when there is an incident which needs investigation. I am fully behind the FA taking up that investigation," Hodgson said.
"I can only congratulate them on this instance of the thoroughness of the investigation. I believe it was eight hours yesterday that Wayne and the people there were arguing the case.
"I am very happy that after that very thorough investigation he has been cleared of charges because I always believed he would be innocent of those charges.
"I have no change in my attitude in that respect, but I think that going through the process, the FA have come out of it well."