The England worldwide was excellent in the middle of the park and played a key role in securing an impressive 4-0 win with Philippe Coutinho, Dejan Lovren, Mohamed Salah and Roberto Firmino getting the goals.
The Egyptian is now the top scorer in the Premier League with an impressive 13 goals after 18 games.
Mohamed Salah made it 3-0 before half time.
The Egypt global has been a revelation in the Premier League this season following his £39m move to Liverpool FC from Serie A giants AS Roma in the summer transfer window.
"As a manager you don't like too much to talk always about Mo; he knows how much I respect him, I like him", Klopp said.
He is a very important player, like the others.
"The front four have been on fire ..."
"Everyone's a quality player and it's up to the rest of us to get in and among it".
"The intensity in the first half maybe we didn't have in the second half".
- Philippe Coutinho has been directly involved in 15 goals in his last 10 away games for Liverpool in all competitions (8 goals, 7 assists).
Two down with only 26 minutes on the clock, Bournemouth were already on the ropes.
Liverpool added a second six minutes later when Firmino stopped the ball crossing the byline by hooking it into the six-yard box on the volley for Lovren to finish with a diving header.
Bournemouth played into Liverpool's hands by taking on the visitors and leaving space behind its back four for the likes of Salah and Firmino to exploit.
Klopp's energetic side had been dominant but eased off before half-time and Bournemouth - who lost Josh King to injury in the 31st minute - would have punished them had Jermain Defoe's 39th-minute effort not come back off the post.
Alex Oxlade-Chamberlain nearly added to the score with a shot which cannoned back off a post in the second half before Firmino glanced home a header from another excellent Coutinho cross to confirm victory.
"I am really pleased about everything", Klopp gushed in his post-match interview.
"We were flat, we never got going".
Liverpool's victory was so effortless as to render the final 15 minutes devoid of nearly any intensity, and this above all will prove Howe's chief concern amid demoralising defeat.
"We were disciplined, I like how we defended different situations, and our tactical discipline was good".