Manchester United put Everton the sword with a third four-goal display from their opening five Premier League games.
Antonio Valencia, Henrikh Mkhitaryan, Romelu Lukaku and Anthony Martial all got on the scoresheet for Jose Mourinho’s side.
It means Everton have now shipped seven goals in their last two games, with today’s defeat coming just days after a 3-0 loss to Serie A side Atalanta.
And Koeman insists today’s performance made him happy – despite the fact they now sit in the relegation zone.
“Sometimes you get more than you deserve,” he said.
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“We made a big mistake at 1-0 and after that it was over.
“From what I saw today from the team it made me happy. More happy than Thursday.
“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.”
Koeman is also hoping Everton’s home form will help see the Toffees become unstuck.
“It wasn’t about ambition, it was about confidence,” he added.
“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.
“They showed us today how clinical you need to be.
“After today we have four home games and we have to win, otherwise we’ll have problems.”