The Red Devils looked destined to secure all three points at Hill Dickinson Stadium after substitute Benjamin Seško put United ahead 2–1 in the 87th minute.
Bryan Mbeumo had earlier opened the scoring for the visitors before Everton fought back.
Speaking in his post-match press conference, Carrick admitted the late heartbreak was tough to take:
“All the work that went into putting us in that position at different stages, to then come away like that leaves us disappointed.
It is not a great feeling, so it feels like a defeat. We got the point, we cannot ignore that, but it feels like we should have had a lot more. It sounds like a cliché to say so at this point.”
Despite taking just four points from a possible nine to open the campaign, Carrick pushed back on claims that United have endured a poor start.
However, conceding 6 goals in 3 games suggests the defence must be worked on ahead of next weekend’s Manchester derby against City.