Murray stunned No.1 seed Jannik Sinner on Thursday (AEDT), however, the three-time grand slam champion lost 6-2 3-6 6-3 to Tommy Paul in Frida's (AEDT) quarter-final.
Currently ranked No.143 on the ATP Tour, Murray had warned the days of him progressing deep in tournaments again were on the horizon after his upset of Sinner midweek.
Murray's career has been ravaged by injuries – the 34-year-old underwent hip resurfacing in 2019 – but the veteran feels he is on the right track.
"My game will improve, I think, over the off season – I'm pretty clear on the things that I need to work on," Murray said, with his focus now turning to the 2022 Australian Open.
"I need to make sure we get a good plan in place that come the beginning of January those improvements have been made."
Paul needed two hours, 16 minutes to see off Murray at the ATP 250 tournament in Stockholm.
"It was a lot of fun," the American said. "He is a legend. I played some of my best tennis today and I even looked over at my coach mid-match and thought it was fun to battle him today.
"It was the game plan to keep him running after his long match [against Jannik Sinner] yesterday. I tried to keep him running. I played tight and stuck to my game plan in the third set."