Sadio Mane opened the scoring in a dominant first half, before goals from the other awful twosome, Salah and Firmino, made sure of the victory in the second half.
"We played against a very good team today, one of the best in Europe and they are showing it, it was a tough test and we learned a lot", Howe said after the match.
Salah meanwhile, proved his detractors wrong when he signed from Roma last summer and he has enjoyed a fabulous debut campaign, scoring 40 goals in all competitions.
Just days after stunningly knocking Manchester City out of the UEFA Champions League on the back of a final 5-1 result over two legs, Liverpool proved that they had no intention of taking the Premier League for granted.
Salah was on target in Liverpool's 3-0 win over the Cherries in the Premier League on Saturday as he became the first Reds player since Ian Rush in 1986-87 to break the 40-goal mark in a season.
"We've come up against a team that without doubt can win the Champions League, but these games are always valuable for our learning as a team", he said.
There were some positives for Bournemouth, who managed to contain Salah fairly well before a header from Trent Alexander-Arnold's cross saw the Egyptian bag his 40th of the season in all competitions.
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"It's completely normal that a boy in that situation wants to be top of the scoring list, the golden boot". "It's also a different season for him".
"It's good and impressive - what a number, wow!"
And just before the final whistle Bobby Firmino got another deserved goal in a sensational season for the Brazilian when Oxlade-Chamberlain played in his teammate.
Salah's goal was his 30th of the season, but asked if the playmaker's tally would be enough to hold Kane at bay, Henderson wasn't so sure.
Jurgen Klopp has put together Liverpool's most entertaining team of the Premier League era and the numbers back it up.
"To win the Champions League is "whissssshhhh" I can't say "woahhh".
City host Swansea next Sunday but could even be confirmed as champions as early as Sunday if United lose at home to rock bottom West Brom.