Inter head coach Antonio Conte said his players should not be downbeat following their 2-0 Champions League loss to Real Madrid as it showed exactly what they must do to reach the level of their opponents.

Eden Hazard's early penalty and substitute Rodrygo's second-half strike in Wednesday's Champions League clash condemned Inter to their first ever home loss against LaLiga champions Madrid.

It is the first time Inter have failed to win any of their opening four group games in the illustrious European competition and leaves their hopes of progressing to the last 16 in tatters.

The Nerazzurri are bottom of Group B, five points adrift of Madrid in second and a further point behind leaders Borussia Monchengladbach with two rounds of fixtures remaining.

Madrid's goals came either side of Arturo Vidal's sending off, the midfielder issued with two quick-fire yellow cards for dissent, which under-fire coach Conte feels was a turning point at San Siro.

"It was always going to be difficult playing against big clubs like Real Madrid, so when going a goal down and a man down, it becomes an impossible mountain to climb," Conte told Sky Sport Italia.

"I think we saw the difference between them and us. It shouldn't knock us down. It should show us there's a path we must take.

"We need to be hungry, hard-working and humble, to realise where we are and not let ourselves get swayed by voices from the outside.

"The only path forward is to work hard and grow in every possible way."

Vidal was unhappy not to have been awarded a penalty when put under pressure by Raphael Varane inside the box and was dismissed by English referee Anthony Taylor after just 33 minutes in Milan.

Chile international Vidal became the third player in Champions League history to be sent off for three different clubs, along with Patrick Vieira and Zlatan Ibrahimovic, but Conte questioned the decision.

"I prefer not to talk about the referee, even if they should be smart not to ruin certain games in this way," he said. "Unless, of course, Vidal has said something very strong to him. He has killed the game."

Inter had just 38 per cent of possession and had only one attempt on target – Ivan Perisic testing Madrid goalkeeper Thibaut Courtois in the final 10 minutes with a weak shot.

Lautaro Martinez and Romelu Lukaku managed four touches in the opposition box between them but Conte does not believe his side have an issue with their attack.

"We're not weak upfront as we score plenty of goals," he said. "We are perhaps conceding a few too many at the moment.

"As I said, the game was immediately an uphill struggle and it became difficult to get back into it due to a red card that was caused by an excessive protest.

"This is the situation, we accept it. We had done much better and were more aggressive in Madrid, but it was tough here to be almost immediately 1-0 down and then see a player sent off.

"That knocked the wind out of us. But nonetheless, I think the team worked very hard today and put the effort in. Don't forget, we were against Real Madrid and not the bottom of the table club."

Serie A hopefuls Inter travel to Monchengladbach in their next group game and host Shakhtar Donetsk on the final matchday.