Cristian Chivu was pleased with the spirit shown by his Inter players in Sunday's defeat to AC Milan, but he accepts his side are losing too many games.

Christian Pulisic's 54th-minute goal gave Milan a 1-0 victory at San Siro as they leapfrogged their fierce rivals into second place in Serie A.

Hakan Calhanoglu had a penalty saved by Mike Maignan as Inter dropped to fourth, with four defeats after 12 rounds of matches.

Inter have now failed to beat Milan in their last six meetings in all competitions and are three points adrift of new leaders Roma.

"When you suffer the fourth defeat in 12 rounds, that is too many," Chivu told DAZN Italia after the game.

"However, the table is still pretty tight. We are up there and need to deal with this frustration, because losing a game like this can leave a mark.

"We hardly allowed any counter-attacks, despite knowing the two strikers could cause us problems.

"The one time we lost the second ball in midfield, they scored. This is football. I take home the good performance.

"The lads kept going to the end, despite the disappointment of conceding the goal, and the frustration after hitting the woodwork twice.

"They tried to score in every possible way, and that is the spirit I want to see."

Inter generated 1.6 expected goals (xG) from a total of 20 shots, compared to an xG of 1.0 for Milan, from seven attempts.

Despite looking the livelier side for large parts, though, Inter were undone by a goal on the counter-attack for a fourth time in Serie A this season.

"I know what we create and what we concede, and these are the risks we take," said Chivu, whose side travel to Atletico Madrid in the Champions League on Wednesday.

"I don't analyse individuals in public. I would never do that. When I see my players give their all in training, I could never point the finger of blame.

"We are all in this and all responsible, for good and bad. We all could've done better; we could've scored earlier.

"Our duty now is to get back on our feet, as on Wednesday we have an equally important match."