Tries from Bruce Douglas and Simon Taylor and seven points from the boot of Chris Paterson saw the Scots rack-up a 17-3 lead by the 22nd minute as Wales struggled to make any impression on the match.
Their forwards were comprehensively out-muscled as the Scottish pack provided veteran fly-half Gregor Townsend with a steady stream of quality possession.
But Wales stepped up a gear shortly before the interval and then began the second half in similar fashion, pushing the Scots onto the defensive as they finally started to win some ball.
They were unable to break through until it was too late - they scored 12 points in injury-time when the match was already lost - but Hansen felt his side's efforts late on were commendable.
"I'm clearly very disappointed with the defeat, especially considering the way we finished the match," said the Wales coach.
"We struggled in the first half, particularly the opening 30 minutes, as they shoved us off in the line-out and kept their composure.
"They had three locks on the field and that worked for them in the line-out. They shut us down and did not let us play in the way we wanted to.
"It was not until later in the half that we actually started to play and then in the second half, when we changed things round, we did well.
"We finished strongly and that makes me a lot happier. (This) defeat has given us another lesson to put in the memory bank."
Wales are now bottom of the championship table and with Ireland and France still to come, they are heavy favourites to take the wooden spoon.
The current team is the weakest for some time as the defeat by Italy in the opening fixture of the championship confirmed, and the national side's predicament is made worse by the fractious club scene in Wales.
Combined with a dearth of world-class players, this has left Hansen with a massive challenge in trying to restore battered Welsh pride.
"The squad we have picked is the best we've got. I'd like 10 more quality ball carriers, I'd like 10 Jonah Lomus but we haven't got them," he said.
"We have to play with what we've got and the boys are getting better. It's a young team and at times we showed we can play rugby. There were lots of tries and lots of movement."