Spurs striker Keane scored against France before the Irish were dumped out of the World Cup by Thierry Henry's handball.
The Ireland captain said: "We deserved to qualify. Everyone could see that - just as everyone apart from the ref and linesman could see Henry's handball. It's just awful.
"We have to regroup and hope the gaffer stays around for as many years as he can because he is a top manager.
"He has out-thought and out-classed managers over the years and did it again on Wednesday. That's a positive note to end on."
Ireland have lost just once in 12 competitive games - to Nicolas Anelka's deflected goal at Croke Park.
Four of those matches were against the teams that competed the last World Cup final - Italy and France.
Trapattoni said: "I came to Ireland because I realised this was a proud nation.
"I knew the players would give me heart, a strong mentality and would believe in our project. They've shown us enormous respect.
"Two years ago, when there was disappointment about losing games in the last qualification campaign, many players said they did not want to come back to the team.
"Now the players know they can play at this level. They believe they can take on France and Italy and beat them. That is the difference."
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