Kompany said: "You like good performances to be rewarded with maximum points, but it's football and these things can happen.
"We know the strengths of Everton and coming to a place like this, it's tough. I felt the team handled it really well, frustrated them especially in the first half and full credit to the lads for that.
"You have to remember we're a newly promoted young team in a really important game coming up against an experienced Everton side with lots of investment. We played with no fear and were brave out there.
"I would say we probably had the upper hand in the first half, but our momentum collapsed twice in moments of our own (goal conceded & red card) but I can not credit the effort of the team overall today."
Kompany added: "Full credit to Everton, I thought they defended really really well. I turned round a couple of times and said they are blocking everything.
"Blocking shots, sliding in, Branthwaite blocked about five and then Tarky (Tarkowski) was doing a job too and they just defended their box really well."