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Conte's Inter are bottom of Group B on two points from three matches and face Madrid again at San Siro in their next European outing on November 25.
Despite Inter winning only one of their last seven games inall competitions, Conte remains upbeat on the back of the narrow loss in the Spanish capital.
"Of course the final result leaves a bad taste in the mouth for me and my players," he told Sport Mediaset. "Games like these show that there is still room for growth, but I don't know how many teams come to Madrid and play this type of game. We went down by two goals and managed to pull it back, and then missed chances to go in front.
"In my opinion my side took more steps today. I really liked the mentality and desire we showed. This team is growing but the results are not rewarding our performances."
Karim Benzema profited from a terrible Achraf Hakimi backpass for Madrid's opening goal, and Sergio Ramos nodded in a second after getting away from his marker at a corner.
Hakimi appeared to be fouled by Ferland Mendy in the build-up to the opener, but Conte did not want to make excuses and instead criticised his side's defending.
"There is little explanation behind the backpass, even if there was a slight foul on Hakimi," he said. "The second goal is similar - we have to improve.There is work to be done and at the moment the little details are costing us in games."
Lautaro Martinez – who became the only player born after 1996 to have scored against both Madrid and Barcelona in the Champions League –and Ivan Perisic dragged Inter back on level terms with well-taken strikes either side of half-time, but Rodrygo's winner now leaves Inter in a perilous position.
"There are still three games to go," Conte said. "That means nine points are up for grabs. We knew this was the most difficult group and we will do everything to get through."
Inter matchedMadrid in terms of shots - 12 -but only managed to get three on target, compared to seven for their opponents who have conceded two-plus goals in five consecutive Champions League games for just the second time after 2001.
Samir Handanovic accepted Inter can have few complaints about the scoreline after failing to make more of the chances that fell their way at 2-2.
"There is a lot of bitterness about this result," the Inter captain told Sky Sport Italia."We had got it back on track and wanted to win - that was the sensation we got on the pitch.
"We had two chances and didn't take them, whereas Real Madrid did, and those incidents made the difference. Ultimately, they were more determined.
"In wins and defeats, there is always something positive to take, but we have to become more determined, because we really felt that we could've won it and that is not the first time we've experienced this situation.