Antonio Conte said Italy deserved to win at Bulgaria despite having to rally back to equalise with a late goal.
Bulgaria led 2-1 after goals from Ivelin Popov and Iliyan Mitsanski washed out Iordan Minev's early own goal. It fell to debutant Eder to curl in an equaliser in the 84th minute to stretch Italy's unbeaten streak to 45 straight qualifiers.
But still Conte, who dealt with death threats in the lead-up to the game, said Italy were the better side.
"In terms of the performance and the chances created, we deserved the victory," Conte told Rai Sport. "It's a shame, as we achieved the bare minimum with the utmost effort in an arena that is traditionally difficult.
"I liked the lads, we dominated the game and [Bulgaria] were restricted purely to counter-attacks."
Defender Giorgio Chiellini reminded the team's critics that Italy have never won a competitive match in Bulgaria before.
"We started so well, but then made mistakes, as we knew that counter-attacks were their greatest strengths and we lost two balls to concede two goals in quick succession," said Chiellini.
"I think we showed grit and determination. It's true we scored late, but we had the chances to get goals much earlier.
"Italy have never won in Bulgaria. We were a little naive to concede those two goals and it turned into an uphill struggle, but this side has ideas, fought hard and tried to the end. We were so close to celebrating what would've been a deserved victory.
"It was a great sign from players like Marco Verratti, Andrea Bertolacci and Eder, who seemed like they had been in the Azzurri for years.
"We would've liked to celebrate a win and get closer to qualification, but we do get some interesting ideas from this game."
Eder was the subject of criticism this week when Inter coach Roberto Mancini said foreign-born players should not play for Italy. But the Sampdoria striker, who was born in Brazil, silenced those remarks at least for the night with his individual effort.
"I am so happy to have helped the group in a venue that has always been difficult for Italy," Eder 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 like Oriundi (foreign-born Italians) in the Nazionale.
"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 at Coverciano. I hope to play more games for Italy."
Italy announced that Inter full-back Davide Santon has been added to the Italy squad for Tuesday's friendly with England after the Azzurri lost multiple players, including Claudio Marchisio, Gigi Buffon, Alessandro Florenzi and Manuel Pasqual, ahead of the Bulgaria match.