Sock advanced when Czech Jan Hernych retired from their quarter-final after he sustained a knee injury during the second game of the match.
"When a guy hits 23 aces and doesn't let you see any second serves, it's going to be impossible to break him," Brown, an unorthodox player known for his touch and outrageous drop shots, told reporters after losing to the 24th-ranked Karlovic.
"You expect this going into the match, but it's still very tough to lose a match like this."
Saturday's other semi-final will be contested by American Rajeev Ram and Australia's John-Patrick Smith, who both won their matches in the last eight on Thursday.
Ram saved two match points before battling past fifth-seeded Frenchman Adrian Mannarino 2-6 7-6(8) 7-6(2), while Smith fended off Japan's Tatsuma Ito 6-3 6-7(2) 6-3.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Larry Fine)
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