The champions maintained their five-point lead at the top of the table, with a game in hand over closest pursuers Rangers and Aberdeen, when they beat Hamilton 3-1 at Celtic Park.
They have another five games this month and Rodgers said: “It’s a really tight schedule but that’s been the case since June.
“Since our first pre-season game, we’ve been training, playing, training, playing – right the way through to now. It’s not an excuse .
“We have to be ready to work hard and press and when we have the ball look after it. I thought in the main that the team did that really well.”
Hamilton boss Martin Canning rued losing two goals just before half-time.
Danny Redmond levelled for Accies after Olivier Ntcham gave Celtic an early lead but quickfire strikes from James Forrest and Scott Sinclair put the home side in control.
Canning said: “Two goals in a minute killed us but we created three or four good opportunities in the second half and, if we’d got it back to 3-2, it would have been interesting.”