The 29-year-old gave his all but was unable to defend his belt - won with victory over Colombia's Darleys Perez last year - for a second time in Manchester.
Linares, who came out on top 115-114, 117-111 and 115-113, offered the fallen champion the chance of a rematch after the bout to leave the door open for another tussle between the two.
It took Crolla a while to get into his rhythm after a slow start, but it was his opponent who made contact with more blows in the closely-contested opening two rounds.
A dazzling combination early in the third for Linares looked to give him a grip on the fight, but the Venezuelan - unbeaten for the past four years - was warned for low blows twice in the following round.
Momentum was swinging Crolla's way in the next two rounds, as he cut his opponent's left eye with one punch and landed a number of left jabs and hooks, but the Englishman was in trouble when Linares made contact with a couple of overhand rights of his own.
It was a case of holding on from that point; the seventh, eighth and ninth rounds doing little to separate the pair before Linares edged the 10th with some eye-catching punches.
A late flurry from Linares in the closing rounds, which saw him throw overhand rights and a flashing left hook, proved to be enough to get the job done as the judges awarded the match in his favour.