Roberto Martinez’s side ran out 3-0 winners at Goodison Park thanks to goals from James McCarthy, John Stones and Kevin Mirallas.

Everton's James McCarthy celebrates scoring his side's first goal during the Barclays Premier League match at Goodison Park, Liverpool.

David Moyes, in his final match as United manager in this fixture last season, accused his players of “rank and rotten” defending – and it was the same scenario this time around.

McCarthy bundled his way past the woeful Paddy McNair and Daley Blind to put the Toffees ahead in the fifth minute and Stones easily glanced in a header to double the hosts’ lead before the break.

And the United back four stood like statues waiting for an offside flag that never came in the second half and Mirallas finished to seal the rout for Martinez’s team, who are now unbeaten in six matches.

After enjoying a run of six wins, Van Gaal has now seen his team lose two successive matches for the first time since he took over.

This was United’s fifth loss away from home and they very much deserved it. Despite dominating possession, they could not find a way through the Everton defence and their own display at the back was poor.

Van Gaal will also be concerned to see Wayne Rooney hobbling off at the end of the match.

Manchester United's Wayne Rooney looks dejected during the match.

United seemed certain of a top-four finish two weeks ago, but now the “rat race” Van Gaal so often refers to is still very much on.

They remain in fourth place – one below Manchester City – and seven points ahead of Liverpool, but Brendan Rodgers’ team have a game in hand.

Last week marked a year since Moyes brought United to Goodison for what ended up being his last game in charge.

Recently all the indications were that Van Gaal had righted the wrongs of the Scot’s dismal tenure.

United have played with width, flair and panache of late, and it had gone under the radar somewhat that their defence had tightened up too.

But in the first half at Goodison, the United back four looked like the shaky defence that had cost Van Gaal so many points early on this season.

It took just over four minutes for their back line to be breached. Everton cleared a United corner and went on a speedy counter-attack. Seamus Coleman raced down the right and the ball fell to McCarthy, who bundled past Blind and McNair before prodding past David de Gea while still off-balance.

Former Everton midfielder Marouane Fellaini, making his first return to Goodison, had the perfect opportunity to respond two minutes later, but cleared the bar from the edge of the box.

Fellaini’s afternoon took a turn for the worse in the 12th minute when he was booked. Shortly after taking out Coleman, the Belgian was penalised for fouling Ross Barkley.

United kept the ball well and some of their passing was crisp. But Everton were happy to sit deep. Luke Shaw and Ander Herrera both saw efforts blocked in the home box and Chris Smalling glanced a header into Tim Howard’s arms.

When Everton countered, United – and in particular McNair – had no answer to Romelu Lukaku’s strength. The Belgian turned the young Northern Irishman with ease and fired a fierce drive at De Gea.

The former Chelsea striker would have doubled Everton’s lead had it not been for a brilliant interception by Smalling.

No United defender was on hand to deny Stones a few moments later, though. The former Barnsley defender – Moyes’ final signing at Everton – leapt to meet Leighton Baines’ corner and the ball flew in despite the efforts of Ashley Young on the line.

Fellaini’s involvement ended at half-time when he was replaced by Radamel Falcao.

Rooney, now playing in midfield behind the Colombian, could have pulled one back for United in the first minute of the second half, but his shot inside the box was blocked.

Despite the change in personnel, United could not find their way through a packed Everton defence and Van Gaal brought on Angel di Maria for the ineffective Juan Mata.

The Argentinian swept in a pin-point cross for Falcao, but Tim Howard clung to the striker’s looping header.

Any hopes United had of a comeback were shot to pieces with 16 minutes to go thanks to more shoddy defending.

Barkley floated a ball over the top of the United back four. They stood still, waiting for the linesman to flag Lukaku for offside, but it never happened. The striker left the ball alone and Mirallas collected before driving past De Gea.

The Spaniard denied Mirallas a second with a superb save late on.

Van Gaal’s afternoon ended on a particularly disappointing note as Rooney hobbled off with an injury and was replaced by Robin van Persie.