Inter toiled for much of Sunday's encounter at San Siro, but D'Ambrosio finally found a way through Genoa's defence three minutes from time to seal the points, with Spalletti's side maintaining their spot two points behind Serie A leaders Napoli and Juventus in the process.
Despite the victory, however, Spalletti felt his side left a lot to be desired with a sluggish display, and though the Nerazzurri are still unbeaten, their coach wants them to go into every game with an aura of invincibility.
"We must create this winning mentality that makes us feel that we can beat anyone," he told Mediaset Premium.
"I always expect more, even when my lads put in a great performance, but we must find our limits and go beyond them.
"We are putting in the effort and the fans flocking to San Siro are creating a great atmosphere too.
"We have demanding fans and that is only right. If at times we don't meet their standards, it's fair that they point that out. We know that the fans love us, even when they might criticise or jeer.
"Today we moved the ball around too slowly, but at least we did move as a team. It was an organised Inter, perhaps too organised, as we needed that flash of inspiration to break through and be unpredictable.
"We should've given Mauro Icardi some more unpredictable service. His qualities are in the penalty area so the potential is there."
D'Ambrosio's winner ensures that Spalletti's unbeaten start continues, but Genoa coach Ivan Juric believes his team were hard done by, citing a foul in the build-up to Inter's goal that was not spotted.
"We put in a fine performance and allowed Inter very little," Juric told Mediaset Premium.
"I have to say, there's so much talk of VAR, but on the corner from which the goal came about, there was a foul on Isaac Cofie.
"In the second half too, there were many free-kicks that only went one way. It's a pity, because we created the opportunities to take the lead at San Siro and were playing better than Inter towards the end."