For 82 minutes, Everton were very firmly in the match despite Antonio Valencia's cracking opener.
Koeman, however, said his targets were unchanged from his debut season at the club when Everton finished seventh and that he needed more time before they could push for a top-four place.
Late goals from Henrikh Mkhitaryan, Romelu Lukaku and Anthony Martial completed a fine win for Manchester United and left Everton in a bad position. However, barring a stunning long range goal in the Europa League qualifiers against Hajduk Split, Sigurdsson is yet to show Everton supporters what all the fuss is about.
Bookmakers Ladbrokes have made Dutchman Koeman their new favourite to be sacked.
Alex Apati of Ladbrokes said: "We've already had one managerial casualty this season, and Koeman could soon become the second if this frightful run continues".
Another player to arrive at Everton this summer was English football icon Wayne Rooney, who is able to play as a striker despite often playing further back.
Koeman's United counterpart Jose Mourinho said that EPL clubs are becoming increasingly defensive and he is glad his side is able to score goals freely this season.
"That is what we tried to do and to get more goals from other players but, yes, it is a big miss that we don't have Lukaku any more but everybody knows that".
"It was nice because I read the programme of United, and my colleague [Mourinho] talked about Everton and spending £140million and that we need to go for the top four".
And it rather summed up the last few weeks for The Toffees when their one-time number ten fired home the third in Sunday's 4-0 thumping at Old Trafford - rubbing salt into the wounds after Wayne Rooney, who moved in the opposite direction, spurned two presentable chances.