The 70-year-old will lead his adopted country into battle with the reigning world champions at Croke Park on 10 October hoping that automatic qualification for next summer's finals in South Africa will still be within their grasp. The Republic trail the Italians, who won in Georgia tonight, by just a point having played one game more, and Marcello Lippi's men face third-placed Bulgaria in Turin on Wednesday night.
While second place might be a more realistic target for the Irish, who have a five-point advantage over the Bulgarians with Montenegro to follow Italy to Dublin, Trapattoni is relishing the biggest game of his latest football adventure to date. He said: "With that result, after this evening, we can think about that, Italy in Dublin.
"Italy is Italy. At the press conference before the first game in Bari, I said, 'We are David and Italy is Goliath'. I think the same. Italy is strong, experienced. I know all players, I know they are great, but 90 minutes is 90 minutes. I am not presumptuous, but why not? It is possible. Football is like that. Never say never."
Ireland were far from at their best in Nicosia despite getting off to the best possible start when Kevin Doyle rifled home a fifth-minute opener. Cyprus levelled on the half hour through Marios Elia and although both sides had chances - keeper Sofronis Avgousti pulled off a superb save to deny Glenn Whelan early in the second half - the game looked to be heading for a draw which suited neither.
However, with seven minutes remaining, Keane made a trademark run to the near post to beat Avgousti to Damien Duff's cross and head home the 40th goal of his senior international career to clinch three vital points.
Trapattoni said: "It was not one of Robbie's better performances, but I know his quality. He is not only our captain, he understands our players, he understands the team. He is a good personality on pitch and I had a feeling he would score a goal."
Winger Aiden McGeady was also full of praise for his captain. He added: "Robbie is a world-class striker. The amount of goals he scores for us is incredible - 40 goals in as many games as he has played (92) is an unbelievable return. Like any striker, he can not be in the game for long periods and then just pop up with a winner, just like he did tonight. He is invaluable to the team."
Keane himself was delighted with a result which keeps Ireland firmly in the race for qualification. He said: "Better late than never. We were obviously delighted to get the three points - that's why we came here. It's crucial at this stage of the group that we get points on the board, and by no means is any game going to be easy between now and the next two. We knew it was going to be tough tonight, but luckily enough, we came out on top."
Cyprus boss Angelos Anatasiades, however, was less than impressed with the Irish side who ended his team's slim hopes of qualification with victory at the GSP Stadium. He said: "They didn't play organised football. All they did was try to hit long high balls at us. It was our worst performance, not just in the qualifiers, but for a long time. It was very indisciplined."