Victory over Feliciano Lopez and Marc Lopez would have seen Murray become the first British player ever to officially top the world rankings, but the Spanish pair spoiled the party with a 6-7(2), 7-6(2), 10-8 victory over the Australian Open champions.
Since the ATP and WTA rankings were introduced in the 1970s for singles and 1980s for doubles, no British player has topped the standings.
Murray reached No.2 after winning his first Grand Slam men's doubles title in Melbourne in January in only his third tournament with Soares.
The occasion looked like it might have got to Murray when he dropped his opening service game but Feliciano Lopez faltered serving for the first set and Murray and Soares dominated the tiebreak.
Lopez and Lopez were the only pair to have beaten Murray and Soares this season, at their first tournament together in Doha. Murray and Soares saved three points to take the second to a tiebreak but made a bad start and could not recover.
That sent the contest into a match tiebreak and Murray and Soares looked good at 5-3 up but the Spaniards fought back.
Murray's next chance to top the standings will come at the Miami Open next week.