Chelsea face Barcelona in the last 16 of Europe's elite club competition in February, but the Italian said his team could be in for another nasty surprise on the domestic front if they made the mistake of looking too far ahead.
Madrid pay the price for a slow start to the season that saw them unexpectedly finish runners-up to Tottenham in the group stage.
No club has won the European title three years running since Bayern Munich in the mid-1970s, underlining how big an achievement it would be if Madrid - 12 times winners overall - won the trophy again in the final in Kiev in May.
So, what did the fans think of the draw?
Liverpool were drawn to play Porto of Portugal.
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Barca and Chelsea will now meet in the round of 16.
"I have to be realistic, we have to face this situation with these players". Hopefully we arrive with a full squad, and have the fortune that you always need in this sort of tie. It's a attractive challenge for the club.
"The first thing for us is to change the final result, because we lost the game against West Ham", he added. I'm happy to play with these players. "We hope we will be strong because we are facing a strong team, an English team that runs and is very physical but also has very good players".
With a potential mid-week replay in the FA cup to begin with, then Conte's men will be making the trip back to Manchester to take on, Manchester City in another Premier league clash.
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