Carrick’s side have just four points from a possible nine over their first three games of the 2026-27 Premier League season.
United were just minutes away from securing a much needed three points when Benjamin Sesko reestablished their lead with an 88th minute header.
Everton kept pushing, however, and deadline day signing Ainsley Maitland-Niles ensured the spoils were shared in added time.
Speaking to reporters after the game, Carrick defended his side’s start to the season as they sit down in 11th.
"We haven't started the season that bad, to be honest," he said.
"It's not that bad, you know. We were that close to coming away with three points today. That's football, little moments that we can deal with a bit better, but we'll be fine.
"We're disappointed, bitterly disappointed to be in the position we were in the game twice, so close to the end.
"All the work that went into putting us in that position at different stages to then come away like that leaves us... yeah, it's not a great feeling, so, it feels like a defeat.
"It's a bit of a cliché, it's the obvious thing to say at this stage, but we have taken a point. We can't ignore that, but it feels that we should have had a lot more."