Cameron Norrie's heroics in Friday's second singles rubber had levelled the World Group first round tie at 1-1 and given the visitors a chance to pull off a shock result in Marbella.
But Murray and Inglot never threatened to maintain the momentum at Club de Tenis Puente Romano as the untested Spanish pair ran out 6-4, 6-4, 7-6 winners in two hours and 28 minutes.
One break of serve in each of the first two sets was enough to give Carreno-Busta and Lopez a commanding lead, with the British pair unable to convert the sole break point they were able to create.
Murray and Inglot dug deep to save two break points in the 11th game of the third set, but quickly fell 5-1 down in the tie-break and their opponents duly closed out the match to take a major step closer to a place in the quarterfinals.
In Sunday's reverse singles Norrie is scheduled to take on Albert Ramos Vinolas and Liam Broady due to face Roberto Bautista-Agut, although both sides are allowed to make changes. Australian Open semifinalist Kyle Edmund, who has been struggling with a hip injury, could be drafted into the British line-up.