Kamil Vacek rifled a shot wide and Reds goalkeeper Pepe Reina saved from Manuel Pamic as the hosts had the better of the early exchanges.
Reina then almost gifted Sparta the lead when he failed to deal with a cross, but he was let off the hook by Pamic, who blazed his shot over the crossbar.
Liverpool boss Kenny Dalglish was forced into a first-half substitution when injured Fabio Aurelio was replaced by Joe Cole, and the former Chelsea man quickly created an opening for David Ngog but the Frenchman’s shot was blocked.
Kuyt then failed to trouble the goalkeeper from close range and, after Leonard Kweuke headed wide at the other end, Reds defender Glen Johnson rant at the defence before curling the ball wide with the outside of his boot.
Reina saved smartly from Kweuke as the hosts looked the more likely to break the deadlock, but Vacek’s shot from the edge of the area, which crept wide, proved to be the final action of note in a dire game.