It was Murray's first defeat since undergoing hip resurfacing surgery in January after he made a triumphant return to tennis by winning the doubles title with Feliciano Lopez at Queen's last weekend.
Cabal and Farah, who are the No. 1 seeds at Eastbourne, also earned their revenge on Murray after the former world No. 1 and Lopez defeated the highly ranked doubles pair in the opening round at Queen's.
Murray will now turn his attention towards Wimbledon, which starts July 1. The three-time Grand Slam champion had joked that he would bungee jump off East Sussex's Beachy Head if he won a second consecutive title this week.
Meanwhile Lopez, who also won the singles title during a marathon effort at Queen's last weekend, withdrew from his first round match against Pierre-Hugues Herbert.
Elsewhere in the men's singles, Queen's runner-up Gilles Simon progressed to the quarterfinals with a 7-5, 6-1 win over Tennys Sandgren. Simon will play Nicolas Jarry after he defeated Pablo Cuevas 6-1, 7-6 (4).