The Magpies went into the game having only lost to Manchester City in the top flight since the middle of December, but goals from Mohamed Salah and Sadio Mane meant that Liverpool were able to cruise to victory at Anfield.
However, Newcastle face a potentially-decisive meeting with Southampton this weekend, and Atsu wants full focus to be placed on the visit of the Saints.
The 26-year-old told NUFC TV: "We wanted to get three points from Bournemouth and against Liverpool, but we couldn't get them so we have to give everything against Southampton at home.
"I believe the fans will be behind us. We fought today, we tried everything, and if we put that determination in the next game, I believe we will get the win."
Newcastle currently sit one place and one point above Southampton in the league standings.