Dundee manager Paul Hartley has described missing out on a top-six finish as a "massive blow".
Goals from Ali Crawford and Jesus Garcia Tena nudged the Dark Blues down to seventh as Hamilton Academical triumphed 2-1.
"It's a real disappointment," Hartley told BBC Scotland.
"I just don't think they performed today - especially the first 45 minutes. They were off it compared to the standards that they've set."
Dundee 'didn't handle' physicality
Hartley's men were 2-0 down at half-time following Crawford's fifth goal of the season and Garcia Tena's penalty.
Gary Harkins came on and pulled one back for the visitors but overall it was an off-colour display by the Dens Park side.
"It's a massive blow for us, we came here with high expectations," said Hartley, who guided Dundee to a top-six finish last season.
"I knew Hamilton would start the game well. We had to handle that and match them and we didn't do that. We didn't stop the crosses coming into the box and we didn't handle the physical side of it.
"We now need to regroup and finish as high as possible."
Hartley remained in the dressing room talking to his players for well over 20 minutes after the match.
"It was just quiet," he added. "We had a chat with them. There were no angry words exchanged. We just had to get our points across.
"It wasn't just this game, it's the amount of draws we've had this season when we've been in good winning positions."
Accies player-manager Martin Canning was delighted to win a first home game in over six months.
"First half we were excellent and could've been further ahead," he told BBC Scotland.
"Second half Dundee came back into the game as they were always going to do. We had determination and spirit to hang on - which is something we've probably lacked a bit of late - but we're back to winning again at home which is important.
"We defended well after we lost the goal, we regrouped."
Twenty-year-old striker Eamonn Brophy had a hand in both goals for the hosts and Canning praised the youngster for an effective shift up front with Carlton Morris.
"He's a talent," added Canning, who felt Julen Extabeguren should have been shown a second yellow card for fouling Brophy in the box to concede the penalty.
"If he continues to develop the way he is now then he's going to have a real good career in football."