Delfini keeper Ivan Pelizzoli single-handedly thwarted the Turin giants' best efforts on goal in an inspired performance, and was only undone by an equally decisive Mirko Vucinic, who scored twice for the home side on the night.
Conte was grateful for the hard-fought win boosting the team's chances of securing a second successive Scudetto, telling Sky Sport Italy: "I’m exhausted and relieved at this success.
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"We’ll take these fundamental points, we know we still haven’t achieved anything, but we’ve taken another step towards our target.
"Vucinic didn’t play well at all but scored twice - just think if he had put in a good performance. I hope these goals are a good omen for [the upcoming Champions League quarter-final game against] Bayern Munich."
The Bianconeri suffered a massive setback during the first-leg defeat by losing 2-0, and Conte has demanded that his men be more adventurous and willing to take their chances in the home tie on Wednesday.
"They’ve won the championship with a 20-point advantage and deserve plenty of congratulations for this achievement," the 43-year-old continued.
"We must be willing to take risks, even to go one-on-one with [Franck] Ribery or [Arjen] Robben. Robben's introduction for [Toni] Kroos [during the loss at Allianz Arena] hurt us then.
"If we want to peg them back, we need to impose our rhythm from the start."