Keane, who is already the top scorer of all time for his nation, made his 126th international appearance against the minnows in a FIFA World Cup qualifier, overtaking Shay Given's previous tally.
He also marked the occasion with a hat-trick as Ireland recorded their second win of the group phase, with a 3-0 triumph at the Aviva Stadium, and Trapattoni was delighted for Keane and claimed he was one of the best players in Europe after five goals in his last two appearances for the Irish.
"I particularly wish to congratulate our captain because for 30 years, I have known the Irish team and the Irish players and for me, he is the best Irish player I have known in 30 years," the Italian said.
"I wish to congratulate him because he scored. At the moment, he is in good form, but I repeat what I said yesterday, he is also one of the best players in Europe."
Ireland are third in Group C with 11 points after the win in Dublin, behind Austria on goal difference only, and the veteran coach was happy with the win, dismissing claims that it should have been used as a chance to boost his side's flagging difference tally of +2.
"It was very, very important to win the game and we won," Trapattoni continued.

"People want five, six, seven, eight goals - it's not so easy, but we played well, particularly in the first half. We had three or four or five opportunities to score.

"The players said to me they had the sun in their eyes and they lost the moment to pass the ball, but after, we deserved to score."