Aston Villa's Ciaran Clark gave the Republic of Ireland the lead in the 35th minute with his first senior strike for his country, despite Trapattoni's men being put under pressure by Poland for long periods.
The Republic - which included just John O'Shea and Glenn Whelan from last summer's Euro 2012 finals - improved after the break and Norwich's Wes Hoolahan added a second in the 76th minute.
It was enough to give the Republic victory in Dublin ahead of their World Cup qualifier with Sweden in March and Trapattoni was satisfied with the competition for places within his squad.
"This evening we needed to see two or three good solutions with the new players," he told Sky Sports.
"In the first half we suffered very much and Poland played very well. But our organisation and balance was very good and I think after the goal, in the second half, we played better and had more personality.
"The new players played very well and we are happy with the result. Poland did not deserve to lose but football is football."
Striker Conor Sammon was handed a chance to stake his claim with a senior debut alongside Shane Long and he drew the praise of Trapattoni, as did James McCarthy.
"Sammon, physically and technically also, he played well but we know we have Shane Long. It was important to see McCarthy because he can grow," Trapattoni said.
"I think our defenders are good enough - we have no other solutions in that position. We don't need to change many players."