Benteke has been returning to fitness following a hamstring problem, and despite scoring the opener in the 1-1 draw with Southampton, he bemoans that lack of killer instinct currently in the side.
Benteke scored his third goal since his summer move from Aston Villa as he came off the bench to give his side the lead against Southampton, only for Sadio Mane to equalise late on to make it a 1-1 draw, denying his new boss his first win in charge at Anfield.
The Belgian told the official Liverpool website: "[One goal] is never enough, you have to play until the whistle. We just let them get one chance and they scored.
"We showed some good things and now we just need to kill the game when we can.
"We are not far but I think it's time to take more points."
One of the reasons for Liverpool's lack of wins so far this season has been something of a lack of cutting edge. Injuries to Daniel Sturridge, Danny Ings and Benteke himself have meant that 19-year-old Divock Origi has started each of the last three games and there has been a lack of cutting edge in the final third, something which Benteke seems to be able to provide as he illustrated yesterday.
One major positive is that he is managing to pick up the odd goal here and there and working his way back to fitness after a slight hamstring problem picked up last month.
He added: "[Injuries are] part of football, that's why when you're out you have to do everything you can to be back with the team. That's what I did.
"That's what I'm working on now, training to be really sharp and 100%."
The games continue to come thick and fast for Liverpool with a League Cup tie against Bournemouth at Anfield on Wednesday night before a huge Premier League clash with Chelsea at Stamford Bridge on Saturday lunchtime as the Reds look to get some much needed momentum into their season.
Liverpool's lack of firepower this season has been a worry as they have only managed to score more than one goal in just the one game this season - in a 3-2 win against a struggling Aston Villa side at the end of last month. For a lot of their draws this season they have managed to surrender the lead against Bordeaux, Sion, Everton, Carlisle and Norwich prior to their draw with the Saints.
It's certainly an issue that needs to be addressed in the coming weeks if the club are to achieve any of their goals this season.