He has been given more chance to work with the squad since Jose Mourinho was sacked last December and United will give him a new deal.
But, despite now leading City by two points, that won't be enough to end their 29-year wait for a title if their rivals also win all of their remaining four games.
They play title-chasing Manchester City on Wednesday, before games against Chelsea, Huddersfield and Cardiff.
"They put their life on us, the team and this club".
Let us know in the comments. "I mean the whole world will be watching Manchester United now". That performance is not good enough for a Manchester United team, from me to players, we let the fans down, we let the club down.
After full-time, we asked Everton fans to vote for their top performers by using our duel-style selector. Now it is in the past and we can not stay on the past because it is a headache.
"United will be a challenge, but it's the old cliché - any game is tough in the Premier League no matter who you play", said Milner.
"They beat us on all the basics".
The French midfielder said that playing in derby games is "beautiful" and "intense" and had been since he was in the United youth set-up. "What we did on the pitch is not respectful for the team mates, for the staff, for the people, for the kit man, for everyone". It is lovely to stop teams in the league or in the world, you just want to beat them because to be the best, you have to beat the best, so I look forward to those games.
"We were beaten on all aspects today and the only place we beat Everton - I can't say we beat them - but we had a fantastic support and I just want to apologise for the performance we turned out".
After the Everton defeat, a number of players have come out to apologize to the Man United fans claiming they will up their game and at the forefront was Nemanja Matic.