The Croatian netted the winner in Saturday's 2-1 come-from-behind win over Sunderland which was his fifth goal of the Premier League campaign.
The goal was Jelavic's first in four outings and now he is determined to continue his run much like the 11 goals in 16 matches he produced last season.
"For a striker, it is always important to score for confidence and for the fans and the team as well, so I hope I can score many more for them," he told the Liverpool Echo.
"Obviously I am pleased to score, but the most important thing was the three points. It was a tough game, with them scoring in the last minute of the first half.
"We were better in the second half and scored two quick goals, so in the end I think we deserved the victory."