The comfortable 3-1 victory in the 228th Merseyside derby made it 10 points from the last 12 and included wins over Everton, Arsenal and Burnley and a draw at Manchester City.
It strengthened their spot in the top four and with all the other Champions League-chasing teams having to play at least one other of the top six - Liverpool have no remaining opponents currently above eight place - there is the opportunity for the Reds to further consolidate.
"It has not been secured (with this result) but it is our target to play in the Champions League," said Can.
"In December, January and February was not our best football but now we are back, we did it in the last couple of games.
"It was very important to win that game. There are still eight games to go and we have to keep it up."
In truth Liverpool did not have to play that well to beat Everton, whose last victory at Anfield came in 1999 and who suffered more than most from injuries on international duties.
Ronald Koeman tried to compensate for the loss of right-back Seamus Coleman to a broken leg and centre-half Ramiro Funes Mori to a season-ending knee injury by switching to a three-man defence in which saw Matthew Pennington made his first appearance of the season.
The 22-year-old academy graduate, in only his seventh senior appearance and first derby, had a mixed day as he scored from close range to equalise a superb individual goal from Sadio Mane but was terrorised by a resurgent Philippe Coutinho at the other.
Liverpool's mercurial Brazilian put his side ahead with a trademark effort and after the break Divock Origi, replacing Mane who went off with suspected knee ligament damage, swept home the third.
Coutinho has struggled for form since returning from an ankle problem in January but his display suggested he has rediscovered his sparkle - impressive after a long trip from World Cup qualifying in South American even if the club did charter a private jet to bring back him and compatriot Roberto Firmino.
"We spoke a lot about the national team and said it's not so cool that they had to leave wherever to go wherever, but obviously I have to say thank you to the whole staff of the Brazil national team because they gave us both boys back in a fantastic mood," said manager Jurgen Klopp.
"It was a world-class goal, another fantastic finish and he made the pass for Div's goal.
Read the full article on eurosport.co.uk: Emre Can: Liverpool back to their best after Everton win