His comments follow the decision by Socceroo head coach Ange Postecoglou to exclude the 36-year-old Neill from a preliminary 30-player World Cup squad to be announced next Wednesday.
Gallop said of the long-serving skipper and two-time World Cup veteran: "Lucas was an exceptional leader throughout the campaign for Brazil and deserves acclaim for his role as captain in Australia's third consecutive qualification for the World Cup.
"In particular, his performance in the crucial away game in Japan was outstanding. On behalf of the football community I thank him for his contribution and wish him well for the next phase of his career."
Postecoglou said the omission of Neill was a difficult decision to make.
"I had a conversation with Lucas regarding the World Cup squad and obviously before I announced the 30-man squad next week I thought it was important for me to speak to him directly," Postecoglou said.
"I informed him that he hasn’t made the 30, from my perspective paying due respect to the fact that he’s been the captain for six years and the captain of the World Cup campaign so far.
"In the end I just had to make a decision not so much about the recent history but the last six months in terms of form and fitness. It was difficult, he’s worked damn hard to get himself ready and available; he’s shown an enormous determination to go to this World Cup."
Neill played 96 internationals for the Socceroos, including a record 61 as captain. He played in all the Socceroos matches in the 2006 and 2010 FIFA World Cups.