Murray had played at the French Open for the first time in three years following a return to the court after battling hip problems, but lost his first-round match in straight sets to Stan Wawrinka.
The veteran Scot was handed a wildcard in Cologne, but was soon up against it as Verdasco, a former world number seven, broke twice to lead 4-1.
Murray rallied to break back before he found his serve under pressure again from Verdasco, who was forced out of contention for the French Open following a positive Covid-19 test.
After saving three break points, Murray, 33, recovered to win the game and reduced the arrears to 4-3.
Verdasco continued to keep the pressure on as he held to move within one game of claiming the opening set.
The 36-year-old Spaniard was, though, made to work for it as Murray forced a break point before then saving two set points.
After another break chance, Murray finally succumbed as Verdasco took the first set 6-4 after almost an hour.
Murray reached the second round of the US Open in September but remains outside the world's top 100.
The Briton memorably came from two sets down to beat Verdasco in the quarter-finals at Wimbledon on the way to his 2013 singles triumph.
However, Verdasco, ranked 61 in the world, showed little sign of relenting in Tuesday's late match in Cologne.
The Spaniard forced the first break of the second set, only for Murray to respond immediately and level at 2-2.
Murray was broken again in the seventh game, with Verdasco appearing to close in on victory when he set up a match point on the Briton's next service game.
The Scot, though, showed he has lost none of his competitive determination to battle back and hold at 5-4 down.
Murray then rallied once more to push Verdasco from the back of the court as he forced three break chances and then saved two match points, the second when coming to the net.
It was, however, only delaying the inevitable as Verdasco eventually served out for the match, progressing 6-4 6-4 after one hour and 40 minutes.