Glasgow took a 10-0 lead, including a DTH van der Merwe try, but Denis Leamy and Murphy crossed over to put Munster ahead.
Colin Gregor responded for the hosts following Donncha O'Callaghan's sin-binning, aided by the kicking of rookie fly-half Duncan Weir, but scores from Niall Ronan and Murphy secured the points for the Irish province.
Lineen criticised his side's inability to retain possession, and was to left rue his side's failure to clear the ball effectively.
"It was the errors that cost us. The boys are disappointed but they were the architects of their own downfall," he said.
"If they had stuck to the game plan it would have been fine, but when we scored some points the re-starts were very messy.
"Munster put a lot of pressure on our kickers at nine and 10 and we couldn't clear our lines. We gave them field position and that is lethal. They didn't have to do much for their tries, which is disappointing."