Trapattoni has come under intense media pressure in this week after Ireland suffered ahumiliating 6-1 defeat to Germany last Friday.
Keane returned to the Ireland side that picked up three important points on Tuesday with a hard-fought 4-1 win against the Faroe Islands.
The Los Angeles Galaxy striker thinks that Ireland must stick together and try to make a success of their World Cup qualifying campaign.
He told Sky Sports News: "He's still everyone's man. Listen, I've said before, it's important we all stick together when you're going through this, important that the whole squad does.
"The lads could easily have crumbled with the amount of pressure they've been under but, fair play to them, they didn't.
"It was a big test for the players after Friday's disappointing result, and it was important we stood up for each other."