Liverpool defeated Swansea City 2-1 to reach the quarter-finals of the cup competition, coming from behind thanks to late goals from Balotelli and Lovren.
Swansea had looked on track for victory at Anfield after Marvin Emnes gave them the lead but Balotelli equalised with four minutes left before Lovren struck in the fifth minute of stoppage time to secure victory for Liverpool.
It was just Balotelli's second goal for Liverpool since joining from Milan and Lovren indicated the Italian striker's scoring drought had been weighing on the Merseyside club.
"I think it's a relief for everyone but I was sure that Mario would score today or tomorrow so it was just a [matter of] time," the Croatian defender told Sky Sports.
"Everyone has confidence in Mario, he's working very hard in training, so it will come with time."
Lovren added he expects Balotelli to produce a run of goals after getting on the scoresheet in the League Cup: "When you score a goal all the heavy weight that was on your shoulders [is lifted]...and I think now his time will come."
After Emnes opened the scoring in the 65th minute with a smart volley on the turn, Liverpool hit back in the 86th with Balotelli prodding a right-wing cross home from inside the six-yard box.
Swansea suffered a serious blow when defender Federico Fernandez was controversially sent off in the 92nd minute but Lovren - who scored the winner with a back-post header - said Liverpool deserved to prevail.
"It was a tough game but we showed today our character," the 25-year-old said.
"I think we played better than the last two games and 100 per cent we deserved this win today."
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