Rodgers said the credit for Celtic's storming start to the season lay with his players.
The Hoops are now unbeaten in 19 games domestically - the best ever start to a season by a Celtic manager in their debut season to eclipse the record of Martin O'Neill.
However, Rodgers, who also led his side to the group stages of the Champions League following a two-year absence and claimed the League Cup, said the credit for Celtic's storming start to the season lay with his players.
"It's very nice and a great mark of the players' concentration, how relentless they've been, their drive to keep going," the Celtic manager said.
"The point I make to them is when you're winning work like you're losing and keep working. Be relentless. If you're going to succeed you have to have drive and desire.
"You need many qualities to keep winning but some of the biggest ones are drive, determination and hunger and we show that in bucket loads."
Celtic had scored nine goals in their previous three games but Hamilton, who had lost 8-1 on their last visit to Celtic Park back in January, made them work harder for their 10th league victory in a row with Leigh Griffiths scoring the only goal of the game in the first half.
It is the first of six games in 18 days for the Glasgow giants and Rodgers says mental fitness will be important at this point in the season.
"The number of games and the level we have been playing at makes recovery important and I think it is very much about that mental fitness," the former Liverpool boss said.
"We all want to play beautiful football and fast-flowing football but we can't always do that. And when you aren't at your best it's about 'can you still win'?
"I think it shows the mark of the team they can still get through that and get the end result which is a victory.
"I think throughout most of this season we've performed at a really high level but some games we haven't.
"Tonight was one of those games that we didn't quite those heights which is sometimes understandable due to the number of games we've been playing.
"But we showed a great desire and persistence to keep going. I thought Hamilton were very well organised. Obviously they've lost a lot of goals here in the past so they were never really going to open up so we had to be patient.
"The pitch didn't help us as it's really slow for the speed of football we want to play but we got the job done in the end and it was a good victory for us.
"I think the boys had to really dig in just to see it through. At 1-0 and with the chances we had the game should have been over long before it was but we saw it through which is a credit to them."