Klopp praised his team for their stunning display but warned that the two-legged tie was only at half-time.
City shredded United apart in the first half, with Vincent Kompany and Ilkay Gundogan scoring in a six-minute span. "This is how a game of football should look", said Klopp. "I could tell you many reasons why we didn't win but we win together and lose together".
"This kind of defence: dominant, not too deep, being in the right area of the pitch so if we win the ball there is a big opportunity for us to use the space they have to leave open", he said.
"Of course we are sad for ourselves, for our fans - but we still have 13 points advantage and goal difference".
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Atletico, the 2010 and 2012 Europa League winners, have now won their past nine matches at the Wanda Metropolitano. But Felipe Anderson and Ciro Immobile, who has now scored 37 goals this season, put Lazio in control of the tie.
"And when you have to defend you have to really defend because they are good". "The door is nearly closed but a little bit open and maybe there is some space for us to get in".
Ahead of this weekend's derby, Guardiola said they must be fully concentrated as they edge very close to being crowned this season's league champions.
"When you analyse the game, it was good, so I can not expect 30 minutes and the opponent doesn't do absolutely anything". If we go two goals up against Liverpool, what happened in the derby could prey on the players' minds. I believe a lot in this team.
City were also shaky in the 3-0 defeat at Liverpool in the Champions League first leg last Wednesday and Guardiola is conscious that their aim to progress to the semi-finals has been made more hard after the scars of the past week.
Manchester United goalkeeper David de Gea demonstrated his world-class ability with a brilliant save from Aguero before the curtain came down on 90 minutes that nearly suspended belief and turned the hope of the home support upside down into despair.
Commenting on the outcome of the game, Guardiola praised his side for their performance but lamented some calls that went against his side.