Glasgow opened up a 27-point gap at the break only to sit back and let the Scarlets back into the contest.
Glasgow held on for a 40-29 win but Hugh told the Daily Record: "We just stopped tackling and handed the momentum to them. Our guys have to learn no team in this league will sit down and die, least of all Llannelli."
Hugh admitted he was puzzled by prop Euan Murray's secobnd-half sending off.
He said: "Apparently the referee saw him stamping on someone's head. I'd be very surprised if that was the case as Euan is the last guy I'd expect to deliberately do something like that.
"We will examine the evidence on video before we decide what to do.