The Sampdoria forward - Brazilian-born with an Italian grandfather - rifled home a spectacular long-range effort with just six minutes of normal time remaining to secure a 2-2 draw on Saturday.
And Eder, whose selection was criticised by the likes of Roberto Mancini – who believes that players born overseas of Italian descent should not play for the Azzurri – was delighted to repay the faith sown in him by Conte.
"I am so happy to have helped the group in a venue that has always been difficult for Italy," he said.
"The coach showed faith in me and I am so happy to have scored on my debut with such an important jersey as the Italy shirt.
"It was a shame about what was said, but I respect Mancini's opinion and many others.
"I think a call-up can happen and it's hard to stay in this squad, I must thank the lads, as they gave me a warm welcome and made me feel important from my first day and I hope to play more games for Italy."
Italy got off to a flying start when Bulgaria's Yordan Minev turned into his own net after just four minutes – but Ivelin Popov restored parity seven minutes later.
Iliyan Mitsanski capped off a quick-fire turnaround when he headed home in the 17th minute, and that looked to be enough for Bulgaria until Eder – a 58th minute substitute –fired in a sumptuous curling strike from the edge of the area.
"In terms of the performance and the chances created, we deserved the victory," added Conte.
"I liked the team, we dominated the game and they were restricted purely to counter-attacks, but unfortunately we could not get another goal."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
