Liverpool's Joe Cole missed a penalty as his side had to make do with a slender first-leg lead over Trabzonspor in their Europa League qualifier.
The Reds went ahead when Cole set up Ryan Babel to finish with aplomb.
The home side then dominated but after winning a penalty for a foul on Lucas Leiva, Cole saw his tame effort saved.
Reds keeper Pepe Reina impressively saved from Umut Bulut before Christian Poulsen was denied a goal for a dubious foul on keeper Onur Kivrak.
Liverpool's failure to capitalise on their second-half chances will leave boss Roy Hodgson in rueful mood going into the return leg in Turkey next Thursday.
Hodgson, whose former club Fulham were losing finalists in last season's Europa League, had stated his priority this season was the Premier League and had consequently sent out a Reds second string.
Steven Gerrard, Glen Johnson and Dirk Kuyt were not even in the home side's squad and Trabzonspor coach Senol Gunes would have had high hopes of earning a measure of revenge over the Merseysiders.
Gunes was the Turkish club's keeper when they were beaten by Liverpool in the second round of the 1976/77 European Cup as the Reds went on to claim their first victory in the competition.
The fact that Gunes is a Manchester United fan would have only added to his motivation.
His side certainly went into the game in good form after winning the Turkish Super Cup - the equivalent of the Community Shield in England - and opening their league campaign with an away victory.
And, apart from keeper Onur Kivrak palming away a Sotirios Kyrgiakos header, the visitors' efforts were seeing them contain Liverpool.
The Reds were almost caught unawares when Burak Yilmaz stole in to win a corner to the near post but he could not get the direction to his header as the ball went harmlessly across the area.
There was a disjointed look about Liverpool in a game which was proving hard work before they broke the deadlock with a moment of inspiration on the stroke of half-time.
Cole produced a surging run from midfield and weighted a lovely pass into the run of Babel, who took a touch before sidefooting high into the far corner.
Cole squanders the chance of opening his Liverpool account
Babel was playing in his preferred striker role as opposed to his normal position on the wing under former Reds manager Rafael Benitez and took advantage of a rare chance which came his way.
However, that was his final action of the match as he was replaced by Fernando Torres at the break and the Spaniard had an immediate impact.
His snapshot forced Kivrak to palm wide and, from the resultant corner, an unmarked Lucas should have done better than to put a 10-yard header wide.
The hosts had now found their stride and their pressure earned them a penalty when Lucas was tripped by Serkan Balci.
Cole, rather than Torres, placed the ball on the spot with thoughts of netting his first goal for the club only to see his penalty parried away by the Trabzonspor keeper.
Milan Jovanovic was also denied his first goal for Liverpool when his low angled shot was saved low to his left by Kivrak.
Liverpool were almost punished for their profligacy and had keeper Reina to thank for maintaining their lead.
Reina's mistake had cost them a late goal in the draw with Arsenal on Sunday but he atoned by getting a hand to Bulut's shot from point-blank range.
Liverpool were denied what appeared to be a legitimate goal when a Kyrgiakos header was only parried against Cole by Kivrak and, despite Christian Poulsen forcing the loose ball in, the goal was disallowed for a foul on the visiting keeper as Trabzonspor held on to keep themselves firmly in the tie.