The world No 50 lost 7-6 (8) 4-6 6-1 by the Swede in Washington in a punishing encounter that lasted ten minutes shy of the three-hour mark.
Murray, 35, suffered from cramps and fatigue – like he did in Newport two weeks ago – in the final set and knows he will have to find a solution if he is to make an impact during the North American hardcourt swing.
“I [have] struggled a little bit with [cramping] the past two tournaments. I need to have a little look at that with my team and maybe see why that is, make a few changes,” Murray said.
“In terms of the training off the court and on the practice court, I'll have to look at that as well and see if there's more that I could be doing, maybe different ways of practising. Scheduling training more in the heat of the day, rather than 10 am when it's not quite as humid, not quite as warm, not quite as helpful. There are a few things I can look at.”
Murray now heads to Canada, where he will look to perform much better at the Rogers Cup in Montreal next week.
“The only positive is now that I get more time to prepare for the tournament in Canada," Murray added.
In an all-British second-round encounter, British No 2 Dan Evans easily defeated Kyle Edmund 6-1 6-2 and will face Taylor Fritz in the third round.