Wallabies skipper Stephen Moore called it "disrespectful" after his side's six tries to one defeat. Gatland told the Guardian he agreed.
"You can be proud but you've still got to show humility and respect," he said. "In the past New Zealanders have prided ourselves on that and been humble about the success of the rugby team."
"Obviously there's history between Steve Hansen and Cheika that's come out on a few occasions, but the squad and team have tried to play things down," he said.
Gatland didn't expect the Lions to be treated the same when they play 10 matches in New Zealand next year but said New Zealand fans could learn a thing or two from the Lions supporters.
"I think it's just something that's between Australia and New Zealand."
"One of the things the Lions fans taught the New Zealand public was how to support a team even when they weren't going well. The Kiwis aren't good at that, when the team's losing we're not good supporters. But the Lions fans were."
The Lions begin their tour against a Provincial Unions XV on June 3 before playing each New Zealand Super Rugby franchise, the Maori All Blacks, and the All Blacks in three tests.