A hat-trick from Troy Parrott, including an injury-time winner, saw Ireland triumph 3-2 on the night and reach the World Cup playoffs.
Asked for his initial reaction, ex-Sunderland and Everton defender Kilbane told Tribalfootball.com: "The overriding emotion is no words. Every Irish supporter feels the same. Honest to God, I must have watched the video probably a thousand times by now. And the reaction videos - pubs, bars, people at home - I’ve probably watched all those a thousand times as well.
"It just shows what the game means to our people. I’ve spoken about it in the last 24 hours: the team and what it means to all of us. It was the most phenomenal week.
"We haven't had a great time over the last ten to fifteen years. It’s been a hard watch at times. Hard going - we haven’t been as competitive as we want to be. But the spirit is still there, and there is quality there as well, I feel. Maybe we’ve undersold it ourselves."
On the performance of AZ Alkmaar striker Parrott, Kilbane believes the performance was historic.
He explained, "The spirit came to the fore this week. God… what a week. There’s been no better, ever - and I can say this with 100% clarity - there’s been no better individual performance across two games than Troy Parrott. Never.
"I’ve played with some incredible Irish players. But to score two against Portugal and back it up with a hat-trick in huge games - huge games - there’s no better back-to-back performance ever in an Irish jersey. He’ll have legendary status for life because of it, and rightly so."
- Kevin Kilbane was speaking to Tribalfootball on behalf of Betway