The Belgian international was shown a red card by Chris Foy for appearing to kick a Swansea City ball boy during his side's 0-0 draw in the Capital One Cup semi-final second-leg clash at the Liberty Stadium.
Some have questioned whether or not the 22-year-old should have been dismissed for the incident, but Gallagher believes that Foy got the decision correct.
"There was a precedent when Liverpool defender Jamie Carragher was sent off for throwing a coin into the crowd against Arsenal at Highbury in 2002," said Gallagher.
"Referee Chris Foy was absolutely correct to send off Eden Hazard, it is violent conduct. He has quite rightly sent him off. He will report it as an act of violent conduct to the FA."
Hazard has since issued an apology to the ball boy.