Roy 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.
Crystal Palace goalkeeper Hennessey denied making the gesture - alleged to be a 'Nazi salute' - in a picture posted on Instagram by his German team-mate Max Meyer as the players celebrated their FA Cup win against Grimsby in January.
The Wales international claimed in a post on Twitter that he was calling out to the person taking the photograph, with any resemblance to the salute "absolutely coincidental", and requested a personal hearing.
Following a lengthy process - which had also seen Hennessey facing a possible sanction for an 'aggravated breach' as it included "reference to ethnic origin and/or race and/or religion and/or belief" - an independent regulatory commission found the charge to be not proven.
Former England boss Hodgson welcomed both the final outcome and the due diligence of the governing body in taking the matter so seriously.
"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.
"They have shown that in an incident like this, which raises doubts, they are prepared to research it, take it as far as it needs taking, and then luckily for us the verdict has been that he is innocent as we have believed all along."
Hennessey had earlier given his reaction following Friday's announcement, saying: "I'm delighted that the FA have found me not guilty of this charge.
"This was a genuinely innocent moment, which appeared to be something completely different when captured on camera.
"I want to state for the record that I abhor all forms of racism, fascism, anti-Semitism or discrimination of any kind."