Carrick knows a positive result away at Fulham on Sunday would give him more time to turn things around during the three-week international break.
There is no real sense that United's hierarchy has lost faith in the manager, who secured Champions League qualification last season before being left short in the transfer market over the summer, reports The Sun.
Manchester United crashed out of a third straight cup competition at the first hurdle and go into the weekend 13th in the table, facing a Fulham side still without a win this season. Ineos gave Carrick only a two-year contract in May, meaning it would represent a striking reversal to sack a third manager in as many years.
The manner of United's two home defeats in four days has nonetheless sent shockwaves through the fanbase. They lost to a Manchester City side reduced to 10 men after 23 minutes, then were beaten by a much-changed Brighton team that became the first visitors in over 50 years to win at Old Trafford after trailing by two goals.
Carrick's players are under pressure to respond, with performances having been consistently poor. United have shown genuine quality for only two spells all season — the second half against Ipswich Town and the opening 10 minutes against Brighton.
The defence has been repeatedly exposed, while strikers Matheus Cunha and Bryan Mbeumo have both struggled.
The decision not to sign a specialist left-back over the summer has also been exposed by Luke Shaw's latest injury, which has kept him out for three matches, with neither Patrick Dorgu nor Noussair Mazraoui able to fill the void adequately in his absence.
United's cup exits this season have followed a similar pattern of promising starts undone by lapses in concentration, a theme that has also crept into their league form. With the international break offering a rare pause in the schedule, Carrick will be desperate to head into it with a win at Craven Cottage rather than a fourth defeat in seven matches, which would only intensify scrutiny on his position heading into the autumn.