Wales led 13-9 at the break, but the hosts scored 20 unanswered points in the second period.
Howley was "hugely disappointed" by his side's second-half display.
"We lacked possession and when we got it, Scotland were hugely effective in the contact area, slowing up our ball or getting turnovers," he said.
"Our changing room was positive at half-time, but that didn't manifest second half.
"Losing today, our championship is over but it's about pride in the next two games.
"Scotland were better than us and deserved the win."
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Wales captain Alun Wyn Jones echoed Howley's thoughts, saying: "We were efficient with our possession in the first half but there was a definite momentum shift.
"We didn't keep possession in the second half and they capitalised on their possession."
Wales host Ireland in Cardiff on Friday, 10 March in their penultimate game before finishing their campaign against France in Paris eight days later.
Wales' Six Nations title hopes are over after Scotland ended their 10-year losing streak against them at Murrayfield, says coach Rob Howley.