Keane was making his 126th international appearance, a record for Ireland, and he marked the occasion in style.
Trapattoni was delighted with the result and praised his captain for another impressive performance in front of goal.
"For me it is easy to speak about him because if you remember what I said about him yesterday at my news conference, he is a great player," the Italian said on Sky Sports News.
"He is the best Irish player. He scores goals and is very intelligent.
"He is clever and at this moment he is also in very good form. For me it is normal to speak well about him."
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.
Trapattoni said: "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."