The former Tottenham Hotspur striker scored twice as the Men in Green thrashed their nine-man hosts to all but secure their place at next summer’s tournament.
The Republic welcome Estonia to the Aviva Stadium on Tuesday for the second leg, but when asked if the tie is over after Friday’s result, Keane replied: “It should be by the way we performed here tonight.
“We can’t take anything for granted but if we don’t reach the finals we’ll be devastated.
“We obviously came here to get a result but I don’t think anyone would have thought what result that was. We got the early goal and managed to kick on from there.”
Goals from Keith Andrews, Jonathan Walters and Keane’s brace gave Giovanni Trapattoni’s side a famous win in Tallinn.
But the Ireland boss is keeping his feet on the ground. “It will be important in Ireland to confirm the result because there are another 90 minutes to go,” he said.
“In those other 90 minutes, we will respect our opponents. They will come with a different mentality, a different attitude and a different performance. We must repeat our performance.”
He added: “I’m not God, I don’t speak English very well – I don’t speak Italian very well – and I make many mistakes.
“But after 30 years in football, I think I understand it a little bit. For this game and on this pitch, I thought Jon Walters would be important to defend the ball and help the team to come up the pitch. Jon showed his quality. We got it right.”
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