The former Red Devils and England midfielder's position was already hanging in the balance as their poor start to the season was compounded by Wednesday's calamitous 4-1 loss at Champions League upstarts Como.
Under-fire Carrick spoke with defiance and hope ahead of hosting Bournemouth, but Sunday's feeble loss extended United's winless run to an eighth-straight match in all competitions and leaves their boss facing the sack.
Rayan and Marcus Tavernier scored avoidable first-half goals for the well-drilled Cherries at Old Trafford, where home fans displayed a banner reading "standards" as the players trudged off at the break.
Roy Keane, Eric Cantona and Bryan Robson featured on the sign brought out of storage for a match that current captain Bruno Fernandes was dropped for days after his critique of Carrick's approach in Italy.
The head coach claimed it was a "pure football" decision rather than punishment for Fernandes, but the world-class star remained on the bench throughout a tepid second half that saw Evanilson punish a wandering Senne Lammens with a third goal for the excellent visitors.
United fans expressed their fury at the Glazers and co-owner Sir Jim Ratcliffe towards the end of a game that brought anger as Bournemouth celebrated a third 3-0 win at Old Trafford in the last four seasons.
"It's a tough situation, there's no hiding from it," Carrick said, deflecting questions about his future.
"What it looks like and what's next I really don't know."
Marco Rose's Bournemouth were superb again, following on from Thursday's famous Europa League win by the same scoreline against an AC Milan managed by Ruben Amorim, whose successor could soon be following him out of Old Trafford.
Carrick applauded the fans, patted his chest and waved on a couple of occasions as United fans chanted his name as he walked down the tunnel, where fury then fixed on the under-performing players that followed him, including the benched Fernandes.
Making United fans' day even worse was Liverpool's continued resurgence with a 2-0 home win over the season's surprise packets, Brighton.
The Seagulls had lost just once this season but that ended in a tight game at Anfield, with Pascal Gross deflecting Florian Wirtz's shot into his own net before Alexander Isak turned in Bradley Barcola's cross, all in the space of four minutes in the first half.
Newcastle beat Crystal Palace 2-0 thanks to second-half goals from William Osula and Harvey Barnes on Sunday, while Lucas Herrington's Hull drew 1-1 with Brentford on the Australian's full home debut.Â
The day's final game ended up with Sunderland being unable to claw their way off the bottom of the table despite earning a point from a goalless draw at home to Leeds.
With agencies
