The Red Devils took the lead twice at the Cardiff City Stadium but were pegged back by a last-minute Kim Bo-Kyung header after slack defending from a free kick.
The Premier League champions twice led in the Welsh capital through Wayne Rooney and Patrice Evra only for striker Fraizer Campbell to peg his former team back in the 33rd minute. Substitute Kim Bo-Kyung then headed a stoppage time equaliser from Peter Whittingham's free-kick.
Not for the first time this season, Moyes's side dropped points because set-piece shortcomings.
"I’m disappointed," he said. "It’s similar to Southampton [a 1-1 draw at Old Trafford last month] where we had the game in our control with a minute to go and conceded from a set piece. It's cost us, ultimately. I thought we could have played better. We didn’t have a lot of rhythm in the second half, but this has been a tough place to come for teams.
"We’re on the back of international duty so I probably would have taken the result however it came today but I'd have liked it [the performance] to have been better, more fluent and it wasn’t to be."
The result leaves United in sixth position, seven points shy of leaders Arsenal – a particular disappointment given the rousing performance that saw off Arsene Wenger's team at Old Trafford before the international break.
United remain unbeaten in their last seven Premier League games, winning five of those, but Moyes conceded their below par start to the season has left them with little room for further slip-ups.
"We've been on a pretty good run but that’s a blow because we can't keep dropping points, two points in games when you’re where we are," he added. "We should have won it. I know we can play better, but we should have won the game."