The Italian expressed disappointment at the result, but said he was pleased with the performance, particularly that of some of the squad's fringe players.
Sky Sports News quotes Trapattoni as saying: "The result gives us great disappointment, but the performance gives us possibilities.
"It gave us confirmation of what we were looking for. [Seamus] Coleman, James McCarthy, [Shane] Long and also [James] McClean, they confirmed against a great team - because Greece are a great team - their quality and their personality, and that was important.
"In the first 20 minutes, we played very, very great football. We conceded the goal and even then, we still had more possession."
The result comes one month after the Republic of Ireland were thrashed 6-1 by Germany in a World Cup qualifier.