The 66-cap winger Kruse, long the Socceroos' whipping boy, suffered a torrent of abuse on social media in the wake of Australia's 1-1 draw with Denmark on Thursday, causing his family to shut down their social media accounts, Australian media reported.
Kruse, who was off his best against the Danes and had little impact going forward, was replaced by 19-year-old livewire Daniel Arzani in the 68th minute.
Centre back Milligan said the Brisbane-born 29-year-old would not be affected by the criticism.
"I think it's much more important what we think of each other than what everybody else thinks of us," Milligan told reporters at the Australians' base in Kazan on Friday.
"When we're out on the field we're the only ones who can help us. We all have a great belief in each other.
"Robbie's been absolutely fantastic for a long time for us and I'm not the only one that thinks so.
"We've got a very very important game coming up. I know he and all of us will be ready."
Australia, on one point in Group C, must beat Peru in Sochi on Tuesday and hope France defeat Denmark to have any hope of reaching the knockout rounds in Russia.
Online attacks have also distracted the Colombian camp, with midfielder Carlos Sanchez a victim of death threats on social media after being red carded for handball in the third minute of the team's opening 2-1 defeat by Japan.
The threats triggered a police investigation in the South American country.
Milligan said his team mates tended to avoid social media during the World Cup.
"It's unfortunate that some people sometimes forget that, at the end of the day, it's just a game and we're doing our very, very best to entertain and to represent our families and our countries," he said.
"It's an unfortunate situation. We tend to stay away from it, we have to have thick skin but it's disappointing that people forget that we never go out to do (badly).
"People are always entitled to their opinion but we don't like to see it go that far."
(Editing by .....)
