Manager Stuart McCall admitted Motherwell had been beaten by an "outstanding" Dundee United side following the Fir Park side's 4-0 home defeat.
Ryan Gauld scored twice as the Tangerines impressed in Lanarkshire.
"I've had almost three years in the job here and that's far and away the best away performance that has been here," said McCall.
"Days like this can happen. We'll lick our wounds, we'll take it on the chin."
McCall had felt getting the first goal would be crucial, with United scoring twice in the first half and adding two more after the break.
"Obviously, you don't want to get beat at home and you don't want to get beat by that scoreline," said McCall.
"We wanted to be better. You've got to just hold your hands up, take your hats off and say we were beaten by an outstanding young side, who were playing at the top of their game.
"We'll put a line through it, you can't look too deeply into that. They've got a really good, talented squad.
"They played some really, really good football. You've got to give them credit."
Injuries prevented McCall selecting Stevie Hammell and Simon Ramsden while fellow defender Shaun Hutchinson was suspended.
And the Steelmen now face a two-week wait until their next match due to the international break.
"We've got to regroup," added McCall. "It's a sore one but we'll certainly be in better fettle when we go to Kilmarnock."