The Bluebirds are three points adrift of safety having played a game more than some of their relegation rivals, and Solskjaer has acknowledged that his team need to continue their improvement of the past few games.
The 41-year-old told reporters: "We know what we have to do and what we're up against.
"Liverpool think that they can win the Premier League, but we focus on ourselves. We've been building and improving over the last few weeks, but we need points."
Solskjaer has won just four of his 13 matches in charge of Cardiff since replacing Malky Mackay at the turn of the year.