The prolific Barcelona forward surpassed Real Madrid legend Raul's tally of 71 goals by scoring his second hat-trick in as many games on Tuesday.
Messi took centre stage after Luis Suarez netted his first Barca goal as the Catalan giants coasted to a 4-0 Group F victory in Nicosia.
The mercurial Messi became the top scorer in La Liga history with a treble in a 5-1 hammering of Sevilla on Saturday and the Argentina talisman revelled in his latest milestone.
"Achieving this record in a competition like this is a wonderful thing. But, beyond that it was a very important game," said Messi, who now has 74 Champions League goals.
Luis Enrique's side face French champions Paris Saint-Germain at Camp Nou next month knowing a win would ensure they finish top of the group and Messi is determined to achieve that goal.
He added: "It will be a tough game against PSG.
"They have very good players and they're growing.
"We'll try to win the group."
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