The Slovenia international had gone 257 minutes without conceding a goal in Serie A before Panagiotis Kone's 12th-minute opener in Sunday's game.
Inter had large periods of possession, but were only able to convert one of their seven shots on target through Jonathan as Walter Mazzarri's side extended their unbeaten run to six matches.
Goalkeeper Handanovic rued Inter's profligacy in front of goal, as he told the club's official website: "We had so many chances and wasted so many of them.
"But if you don't score then things get difficult. In games like these it often happens that, if you score first, things turn out differently.
"But sometimes you even lose games like these.
"We need to be positive and move forward."
Inter face the club's former assistant manager Sinisa Mihajlovic next when Sampdoria head to San Siro on Sunday.
