Offensive chants directed towards the 64-year-old led to an incident between the two parties, which saw Redknapp confront the home support.
UEFA confirmed that would consult the referee's post-match report before taking action, but with the incident not mentioned by the official, the governing body have deemed the matter closed.
Speaking on the incident after the game, Redknapp said: "Did I make an 'obscene' gesture? No, I didn't make... No.
"I have spent enough time in Ireland to know what lovely people they are.
"If you go and meet them afterwards they are probably lovely people. But they get together and shout a load of nonsense and that is football. That's life. I don't hold any grudges."