Bryan Mbeumo and Benjamin Šeško put United ahead either side of a Tyrique George goal, only for Ainsley Maitland-Niles to snatch a dramatic 96th-minute leveller and secure a 2-2 draw at Hill Dickinson Stadium.
Marcus Rashford and Luke Shaw caused problems throughout for Manchester United down the left, with the pair combining for Šeško's goal before Rashford was withdrawn in the 70th minute after "feeling a bit of something."
Speaking to reporters after the match, Carrick did not hide his frustration at failing to see out the win.
"Yeah, we're disappointed, bitterly disappointed. To be up in the position we were in, leading the game twice and so close to the end. And all of 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," he said.
"Feels like a defeat, bit of a cliché, the obvious thing to say at this stage, but we have taken a point and we can't ignore that, but it feels like we should have a lot more."
Asked about a pattern of conceding two goals in every game so far this season, Carrick pointed to the quality of the finishes rather than a deeper structural issue.
"The mentality is there. I think there's obviously things we need to get better at as a team. That's two strikes from distance, really, two really good strikes from their point of view, so sometimes they fly in the top corner, and more often than not, they probably don't, so there's a little bit of that," he said.
"But yeah, obviously we can't ignore it. We need to concede less goals to give us a better chance of winning games, but we'll certainly look at that and keep improving."
Carrick pushed back on the notion that United's start to the season had been below expectations, despite the club sitting on four points from three games. "We haven't started the season that bad, to be honest," he said. "We were a lot closer to coming away with three points today. That's football, there are moments that we can deal with a bit better, but we'll be fine."
The head coach also praised Rashford's contribution before his withdrawal.
"He's done very well. As I said during the week, he's done ever so well since he came back. I thought he looked really sharp again today and dangerous. That final little moment didn't quite drop for him, but nevertheless, I thought he created really good opportunities, and there was a big threat throughout the game," Carrick said, also crediting his combination with Shaw down the left.
"Marcus and Luke were particularly dangerous down that side."