Dundee United manager Mixu Paatelainen questioned the mentality of some of his players after losing a lead for the second week in a row.
Hamilton scored twice after Billy Mckay had given the home side the lead to leave United seven points adrift at the foot of the Scottish Premiership.
"Totally astonished how we lost that game," Paatelainen told BBC Scotland.
"Scored a wonderful goal, the game is under control no problem. I must also question mentality."
Mckay had a great chance to extend United's lead before Hamilton's equaliser.
"After going 1-0 up, we create chance after chance after chance - clear-cut opportunities," said Paatelainen.
"One-on-one with the goalkeeper, you don't put them in the net then you pay the price. You're asking for trouble.
"There's one or two people there who, when 1-0 up and miss opportunities, they start going a bit shaky and asking for trouble we certainly don't need."
It was the second week in a row that United had gone ahead at home only to lose all three points, with St Johnstone winning at Tannadice last time out.
"Both matches I feel we should never have lost," said Paatelainen. "I think both matches we should've won, but we are where we are.
"It is very difficult to turn round, but we will. We have enough to turn it around.
"We just have to make sure that, when we create those chances, we put them away and put the game to bed."
Paatelainen bemoaned an ultimately weak defensive effort, with United having earned only two clean sheets all season.
"When it comes to passing the ball and creating chances we've got plenty now to win a match," he added.
"It's the defensive end, we must be much more solid and determined to defend our own goal."
Hamilton, for whom Ziggy Gordon scored the winner after Gavin Gunning appeared to score an own goal to level the match, regained their position within the top six.
Player-manager Martin Canning was delighted with the character and commitment his side showed.
"The lads' character again is second to none," he said. "They never know when they're beaten and they continue to work.
"It probably wasn't our best performance, but in conditions like that in a difficult game, it was never going to be easy."
Despite their lofty position, Canning reiterated that Hamilton's main goal is to remain in the Premiership.
"Our main aim is to make sure we're a Premier League club next year," he said.
"To go 14 points ahead of the team at the bottom is massive for us.
"We've got to continue winning, continue playing well and, if we do, hopefully we can continue to win games."