The 74-year-old manager was content with his side's performance as they eased past the Faroe Islands and praised the LA Galaxy striker as he brought his international tally to 59
The 32-year-old marked the occasion in style as he scored all three goals in the comfortable victory over the Faroe Islands at Aviva Stadium on Friday evening as Ireland climbed to third in World Cup qualifying Group C.
And the Italian tactician was quick to praise his top marksman at full-time.
"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," said Trappattoni.
"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."
Trapattoni was satisfied with a victory which at least keeps alive his team's hopes of finishing second in the group behind runaway leaders Germany.
He added: "Obviously this evening, it was very, very important to win the game and we won.
"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."
The hosts dominated the majority of the game and Wes Hoolahan, on his first competitive start for his country, was another who impressed. When asked whether the Norwich playmaker would feature against Sweden in Stockholm, Trapattoni refused to say but admitted he was impressed with his performance.“In this moment he played well. I already said he’s a great player but in the past we had a squad of players and we achieved qualification for the Euros. Hoolahan, McCarthy, Whelan. Whelan is an important balance for one or the other. Experience is important also,” he said.
The Boys in Green conclude a busy end-of-season schedule with a glamour friendly against Spain in New York on Tuesday and the manager was quick to confirm all his players would be boarding the plane with the exception of Marc Wilson through injury and Aiden McGeady and Shane Long because of other commitments.
Friday's result keeps Ireland's hopes of qualifying for back-to-back tournaments on track but Austria's 2-1 victory in Vienna over Sweden means the race for second place intensified further.
Asked if he was surprised by the result in Vienna, Trapattoni said: "No, because Austria are a good team. I was in Austria and I know many players.
"Without a silly mistake, we could have won [against Austria in March], but they are a good team and they have good players.
"But we are at the same level. Without this silly 90th-minute goal, we deserved to win and we could have been in second place behind the Germans."