For all Liverpool's dominance, they only had one goal to show for it in the first half as Salah continued to be frustrated, with Steve Cook's brilliant challenge denying him.
Drogba achieved the record by scoring 29 goals in the 2009-10 season to help Chelsea to a treble, and it was equalled a fortnight ago after Salah got the victor against Crystal Palace.
He is only the third Liverpool player in history to hit this landmark after Ian Rush and Roger Hunt.
Manchester City may have been crowned Premier League champions yesterday but fans of Liverpool have also had plenty to shout about this year. "I'm sure he'll keep doing that for the rest of the season".
"When we lost the ball we were like lions, coming back with counter pressing, that obviously makes life uncomfortable for the other side", said Klopp, whose side have now scored 78 league goals this season.
"If I had a choice between the Champions League and the Golden Boot, then of course it would be the Champions League, no doubt the Champions League", Salah told Liverpool's official website.
Mohamed Salah took his tally for a remarkable debut season at Liverpool to 40 goals as Jurgen Klopp's men suffered no after effects from their efforts in reaching the Champions League semi-finals in midweek with a routine 3-0 win over Bournemouth.
'I can not lie - it is in my mind, ' said Salah. I know the reason is we come here together to win things but I think the way you try to do it is important.
Bournemouth briefly threatened when Dan Gosling's shot brought a smart diving save out of Loris Karius but that was the best they could offer on a day when Liverpool won comfortably without breaking sweat.
"It's like that but, in the end, we play as a team".