The Azzurri produced a smash-and-grab raid to defeat one of the Euro 2016 favourites on Monday in Lyon, where Emanuele Giaccherini's well-taken opener and Graziano Pelle's late counter-attacking strike sealed three vital Group E points.
Conte rejected out of hand the suggestion Italy's victory could see them - having been largely written off - now considered among the leading contenders to lift the Henri Delaunay Cup.
And the former Juventus boss has demanded supreme focus from his players to avoid a repeat of their fate in Brazil in 2014, when Cesare Prandelli's men defeated England in their opening game only to fail to progress after losing to Costa Rica and Uruguay.
"I don't think a single game can change people's assessment. People who think that [we can now win] know nothing about football," he said.
"We still have an open wound from the World Cup.
"The memories are very fresh of two years ago when our first game was an excellent performance and then we went out in the group stage.
"We want to make the last 16 and then get as far as we deserve to go."
As for accusations this Italy team lack the star quality of their predecessors, he added: "Even in the tough times, I believe when supporters see the players giving their all on the pitch, willing to spill blood, sweat and tears, I believe they really appreciate that, regardless of what they have in terms of talent."
The passion felt by the Italy players was evident when Pelle sealed the points, as the unused substitutes and coaching staff joined the players on the field in wild celebrations.
But the close bond among the squad has come as no surprise to their coach.
"I've been saying so since the start [of my tenure]," Conte said of his team's spirit.
"I don't tell lies. I'm not saying it for the sake of it. This is a squad of men and of good footballers. That's very important because in competitions like this is when the players start to enjoy being together.
"Nothing is written in football. Not at the start, not on paper. Everything needs to be decided on the pitch with deeds rather than words. We need to be really prepared in everything we do and everything we work on in order to bring happiness to ourselves and indeed our fans."