The Italian side are plying their trade in the Magners League for the first time this season and have already beaten former European Champions Leinster as well as Glasgow and Newport Gwent Dragons in the Celtic competition.
And having seen Saturday's opponents come so close to one of the biggest shocks in Heineken Cup history at Leicester's expense, Castrogiovanni was understandably full of praise for his compatriots.
"It was really close from start to finish and they played great. We came here knowing that, if we didn't play our best game, we could lose. We didn't and we were lucky to win," Castrogiovanni told the Leicester Mercury.
"They kept going forward and had a massive defence and good set-piece.
"With five minutes to go, I thought we would lose. If Alesana had not broken the line and scored, we could have easily lost the game.
"We had more experience of these big European games and that was important in the end."
Leicester will be back at Welford Road for next weekend's second round as they welcome the Scarlets to the East Midlands.
The Welsh side came out on top in a nine-try thriller against Perpignan in the other Pool 5 encounter at the weekend.
Treviso travel to face the French outfit at Stade Aime Giral on Sunday, October 17 looking for a repeat of the historic home victory they secured against the same opposition last season.