In their first match in Europe's premier club competition for five years, the Reds went 20 minutes without threatening the Group B minnows from Bulgaria.
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It was the in-form Raheem Sterling, recalled to the side after being rested for the defeat to Aston Villa on Saturday, who got Liverpool going with a run down the left which finished with a blocked shot.
A chance for Mario Balotelli quickly followed as the Italian striker turned his marker cleverly on the edge of the box before seeing his shot thwarted by a brave sliding intervention from Aleksandar Aleksandrov.
Persistence on the edge of the box saw the £16m signing from AC Milan fashion a chance for himself later in the half, and he saw debutant Milan Borjan tested for the first time as the Ludogorets keeper dived to save low to his right.
The hosts knocked on the door more heavily as the interval approached, with a clever reverse pass from Sterling starting a move which ended with Adam Lallana wasting two great chances to score from close range.