Immobile scored the first goal of the Conte era within three minutes of it beginning, sending the hosts in Bari to a 2-0 win over World Cup semi-finalists the Netherlands.
The Borussia Dortmund man said the Italians delivered for the former Juventus coach.
"I am happy with my first official goal for Italy. The game went the way we had prepared for it and we did what the coach asked," Immobile told Rai Sport.
"The team was concentrated for the whole 90 minutes and fortunately it went well."
The 24-year-old combined with Conte previously at Siena in 2010-11, and said his experience helped him appreciate the game plan.
"I know the coach well back from our time at Siena. He's the same old 'hammer' and that's only right that he forces the players to give their best. We are symbols for Italy, after all," Immobile said.
"Fortunately I had already worked with Conte at Siena and last season at Torino we played the same movements with [Alessio] Cerci under Giampiero Ventura.
"I tried to help [Simone] Zaza, who had never worked with Conte before, to get the right movements."
Italy will look to preserve their winning form when they travel to Norway for their Euro 2016 qualifying opener on Tuesday.
‘Scoring in a World Cup is like winning the title – can you imagine millions of people celebrating something you did? It’s insane and made me very proud’: Brazil legend explains how much 2002 goal meant to him
'He already had the ability but didn’t use it because he was afraid to shoot – I said, "You’re a player who has to decide games – you have to take risks, mate"': Liverpool star was forced to become confident by team-mates
