Eder netted his first goal for Portugal in the 52nd minute to help end a 39-year wait for a victory over Italy.
Leonardo Bonucci had hit the post for Italy minutes earlier.
The result will be a blow to Italy's hopes of being seeded in the draw for 2018 World Cup qualifiers. The draw, which takes place on July 25, is expected to use the next FIFA ranking to create pots.
"I don't know why Italy is behind some nations," Conte said. "Obviously it's because of previous eras. We have worked hard, but there is still a lot to work to do. There is a change in generation, but these games help you grow."
Both teams came into the match after moving closer to securing qualification for the 2016 European Championship at the weekend. Italy drew 1-1 in Croatia, while Cristiano Ronaldo netted a hat-trick as Portugal came from behind to beat Armenia 3-2.
Portugal has a woeful record against Italy, having won just four out of the previous 24 matches between the two nations. It had only managed one draw in 11 matches since its last victory in 1976.
Italy, which was missing several players through injury, should have taken the lead in the 27th minute, when Stephan El Shaarawy cut in from the left but curled his effort just past the base of the far post.
Portugal went even closer minutes later following a howler by Salvatore Sirigu. The goalkeeper, who was standing in for injured Italy captain Gianluigi Buffon, failed to control a backpass. Eder snatched the ball off him and set up Valera to fire towards the empty net but Andrea Ranocchia scrambled back to clear the attempt off the line.
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