Antonio Valencia scored a stunning half-volley after just four minutes to send United on their way.

Everton then battled bravely until deep into the second, where Henrikh Mkhitaryan, Romelu Lukaku and Anthony Martial all got on the scoresheet for Jose Mourinho's side.

The defeat is Koeman's fourth in a row but the Dutchman was refusing to be downbeat after the drubbing.

"From what I saw today from the team it made me happy. More happy than Thursday," Koeman told Sky Sports.

"We are still afraid. We dropped too much back.

"Sometimes you get more than you deserve. We made a big mistake at 1-0 and after that it was over.

"We grew in the game and in confidence and not many teams will get two big chances like we got today. We didn't score the goal and after a personal mistake it was 2-0."

And Koeman believes his side need to start believing in themselves again.

"It wasn't about ambition, it was about confidence," he said.

"I tried to shout to them, especially the full-backs, to take a higher position but that's what's in the head of players after a tough period.

"It's hard for a manager. When the whistle starts it's all about them. We started too afraid."

This is the Toffees' worst start to a season in seven years.

But the club will be relieved to have got some of the toughest fixtures of the season out of the way early on.

"After today we have four home games and we have to win, otherwise we'll have problems," concluded Koeman.

Everton welcome Championship strugglers Sunderland to Goodison Park in midweek.