Healy pretended to play a flute after coming on in the second half of the 3-1 win over the Scottish champions.
Gascoigne's actions were viewed as provocative because Celtic's fans are usually sympathetic to the Irish nationalist cause and he was fined £40,000 by the Ibrox club.
But Healy's agent, Stephen Hughes, insists his client was merely responding in kind after he was targeted by the visiting supporters at Craven Cottage.
Hughes told the Daily Mail: "David has told me he was wearing boots with a Northern Ireland flag on the back.
"They had been made for him to celebrate being the leading scorer in the Euro 2008 qualification matches.
"They were chanting, 'Where were you on the 12th', which is the day of the Orange marching bands in Belfast.
"So he simply pretended to play the flute - there was no attempt to inflame the fans.
"Afterwards, some of the fans who had been giving him stick sent over programmes for him to sign which he did quite willingly."