The Briton, 34, had won his two past matches against world number 33 Bublik, most as of late in Rotterdam last month.
Be that as it may, Bublik, 24, demonstrated excessively solid for the previous world number one on Sunday, winning 7-6 (11-9) 6-3 in California.
"I simply didn't pursue my open doors today, and I feel that was an open door missed," said Murray.
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The primary set went with serve yet Murray, presently positioned 88th, scorned three break focuses while driving 2-1 up, and one more at 3-2 up.
Then, at that point, in the sudden death round, Bublik won in the wake of saving three set places and Murray neglected to enjoy another two reprieve focuses in the principal round of the subsequent set.
Bublik then, at that point, truly found his notch, going 4-1 up subsequent to asserting the match's just break of serve.
Murray did well to clutch his make it 4-2 and kept on battling to remain in the match, however Bublik saw out the success to arrive at the third round.
That likewise left Murray without consecutive successes since arriving at the Sydney Exemplary last in January.
"Against players that have large serves and are difficult to break, you really want to - whenever you get those possibilities - be savage," added Murray, who procured a trump card for the Experts occasion and partook in his 700th win on the ATP Visit in the first round.
"I simply didn't exactly play alright in those minutes today and that is what clearly I need to pivot."
Investigation
BBC tennis reporter Russell Fuller
Next stop Miami for Andy Murray, where he trusts [recently reappointed coach] Ivan Lendl will actually want to observe a portion of his matches nearby.
Murray is as yet on the lookout briefly mentor, who might be ready to go with him for 20-25 weeks every year. He says the preliminary before the end of last year with Esteban Carril went quite well, yet the Spaniard didn't have that kind of time accessible.
The LTA mentor Imprint Hilton, who worked already as a voyaging mentor with both Dan Evans and Kyle Edmund, has been with Murray in Indian Wells and will go through the following week preparing with him in Miami.
Murray says their time together has been both positive and charming. No discussions have yet been held about whether that organization could turn out to be more long-lasting, yet in Murray's eyes, he appears to be a solid applicant.
Third seed Zverev beaten
Somewhere else, third seed Alexander Zverev is out after a three-set rout by American Tommy Paul, who recuperated from 4-2 down in the last set to seal a 6-2 4-6 7-6 (7-2) triumph.
German Zverev was playing his first ATP competition since being tossed out of the Mexican Open and allowed an eight-week suspended boycott for striking the umpire's seat the month before.
Zverev's leave implies Matteo Berrettini is presently the most noteworthy positioned player in the base portion of the draw. The Italian 6th seed beat Denmark's Holger Rune 6-4 4-6 6-4.
Andrey Rublev, cultivated seventh, is likewise through to the third round subsequent to facilitating past Germany's Dominik Koepfer 7-5 6-4.
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