Kompany is now looking for them to start putting together performances and victories away from home - beginning with Fulham in their next outing.
"I think at home we have proven that we are an incredibly tough team to beat and we can score goals of course," Kompany told BT Sport.
"It was a great game for the fans and it was just end-to-end and at times the tempo was frightening.
"We looked to be in control of the game for the most part of it and there were a lot of stand-out performances obviously from our team but collectively I think we've done incredibly well."
He added: "The biggest message is if we win the next game which is Fulham away.
"Those are the games that are very difficult for us. Home games we'd like to challenge anyone and like you see today it is a real fortress here."
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