This season Claudio Ranieri's men have started by collecting four points, winning once, from their opening three games and currently sit ninth in the table.
"After last season it was always going to be hard. After a few games, whatever we did, people were going to compare to last season and say it's a slow start," King said.
"But now we have our first win, we can hopefully get up and running. Winning at Anfield would be a real statement.
"We know it's going to be tough because they've had a good start themselves, but we know if we play the way we can, then we can be a match for anyone."