Jonathan Ikone scored twice as the Viola eventually won 4-2 after the Swiss had brought the scores level at 2-2.
"I am fortunate to have a great staff, so we study where we can hurt our opponents and have a refresher at half-time,” Palladino told Sky Italia.
“We analyse the data and then see what we can do better. Often we see a strong response from the team, just like the one we had today. I am happy with the reaction, the lads did really well.
“We had the right approach in the first half too, but we knew that St. Gallen press hard, especially on home turf. We lacked fluidity in the first half, but did better in the second with Ikone and Sottil raising the quality level.
“It was not easy to react like that and I congratulate my players, they deserved the result with a fine performance.”