Goals from Steven Pienaar, Andros Townsend, Jermain Defoe and Harry Kane gave Tottenham a resounding win over the Irish part-timers, but Rubin Kazan's 1-1 draw at PAOK Salonika meant Redknapp's team crashed out of the Europa League.
The 64-year-old's night took a turn for the worse with 20 minutes left when he appeared to make the angry gesture towards the Shamrock fans but, when asked if had made an obscene gesture towards the Rovers fans, he said: "Not really. Did I make an "obscene" gesture? No, I didn't make... No."
Redknapp had taken heavy criticism from the Rovers fans all night, but tried again to play down the incident by saying: "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."
The defeat meant Shamrock ended their first full European campaign without registering a point.
The Irish champions did play well at times, however, and came close to grabbing a consolation goal on a number of occasions.
Departing manager Michael O'Neill, who is believed to have an interview for the vacant Northern Ireland job next week, admits Spurs were a class apart.
"We were playing against a better team with better players," he said. "I thought we played well in the early part of the game but the goal set us back.
"It's disappointing. In the second half we did well, but we have to be honest and say we were well beaten by the better team."
Source: PA
Source: PA