The summer signing from Celta Vigo has yet to break his duck in four league appearances and after three successive starts was dropped to the bench for Monday's draw at Swansea.
A shoulder injury to Philippe Coutinho which will keep the Brazilian out until the end of October means Spaniard Aspas could get a recall at home to Southampton on Saturday.
The 26-year-old is looking to get his Reds career up and running with that all-important first strike and knows he has to improve.
"Over the last four or five seasons I probably haven't gone as many games as this without a goal," he told liverpoolfc.com.
"I've never been an out-and-out goalscorer but it's true that over the last three seasons I have scored quite a number of goals.
"I suppose on a personal level I'm not as entirely happy as I would want to be because I still feel that I can do a lot better.
"I'm working hard every day to try and improve and be able show that on the pitch to my team-mates.
"It's not that easy coming here from the Spanish league but I've only had a short period to settle in.
"But being on target isn't so important as long as the team is winning and stays at the top of the table.