The 2-1 reverse sees Inter dumped to the Europa League.
“We had the chances to win the game, we created those opportunities, but lacked that clinical edge to convert them," the coach told Sky Sport Italia.
“I have no complaints to make, as my players gave their all. We just lacked a goal and instead conceded at the other end to go 2-1 down, which really killed us.
“Watching that Ansu Fati goal is painful, as it killed us in every way. We were pushing, creating the chances to score and go 2-1 up. It's disappointing above all for the players, as they are giving their all in a difficult period.
“I was also disappointed for the fans at San Siro, as they pushed us from start to finish and created a wonderful atmosphere. It should've ended differently.
“Looking at the group and our overall performances, I think we deserved more. However, when you don't get out the other side, you need to roll your sleeves up and keep helping these lads to grow. It's all valuable experience.
“We need to get back on our feet and start walking again."
Conte continued: “We wanted to continue in the Champions League and felt we deserved it. There is disappointment from everyone right now, but as I told them, we have to raise our heads again.
“The team is doing remarkable things in a tough period. We have two games to go before the Christmas break and hopefully we can recover some players from injury. In this emergency situation, they did so well to cover the gaps.
“I saw a lot of disappointment in their eyes and I was sad about that."