The previous mark of 62 set by Willie Maley's Celtic side between November 1915 and April 1917 had been ended by Kilmarnock, who were in the mood to finish another run by the Bhoys' modern 'Invincibles', who currently lead the Premiership.
"The players deserve all the credit they get," said Rodgers afterwards.
"It's a 100-year-old record. If you take it over the piece, over 17 months, to get to 62 games -- and I think win 56 those and draw six -- it is a phenomenal achievement and shows the level the players play at."
His side now have a chance to take the record outright when they play at St Johnstone in the league next Saturday.
(Reporting by Ian Chadband; Editing by Christian Radnedge)
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