Burton knocked over four penalties and a drop goal in response to Warriors' fly-half Duncan Weir's early try for a narrow 15-13 win.
And Zatta insists it is up to Treviso to follow up that result with a second consecutive win when they welcome the Scarlets to Stadio Monigo next weekend.
He said: "I appreciated the sacrifice and the win-at-all-costs attitude of the players.
"It was a Benetton team with lots of youngsters, especially in the backs with [Alberto] Chillon, [Tommaso] Iannone and [Luca] Morisi, who were well led by [Ezio] Galon and [Ludovico] Nitoglia.
"Clearly if you don't feel the pride of playing with this jersey, you won't be able to win away from home."
And while Treviso have been decimated by the loss of 13 players to the Rugby World Cup, the performances of scrum-half Chillon, centre Morisi, and winger Iannone, all in their early 20s, has given hope for the future.
Zatta insists the side are delighted to have so many players away representing the national side, even if they had struggled to hit the heights of last season prior to the Glasgow success.
"As Italians we are proud that our players are being picked for the national team," he said.
"Besides the response we got from the Scottish fans made us proud. It means we are working hard."
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