Daniel Sturridge scored the only goal of Sunday's game after just four minutes as the Reds went top of the Premier League with a third straight win.
Manchester United enjoyed a lot of possession but Liverpool held firm to keep their perfect defensive record intact, and Rodgers was keen to stress after the match that it was his players' attitude that helped them at the back.
"Our mentality was key. We didn't play as well as we have and Manchester United played some really good football, but our defensive mentality gets better all the time," he told Sky Sports.
"The resolve we have in the group was evident."
With Liverpool's extra-time cup win over Notts County taken into account, the Reds have won four from four this season.
"The players have been outstanding," Rodgers added.
"We worked hard in pre-season to get this start. We have four from four and we are getting the rewards for how hard we're working.
"I am so proud of them."
Rodgers' joy was certainly shared by the Liverpool owner, John W Henry.
"Terrific win; terrific start for the season. What a match! Poised and smart play against United. Team effort, superb desire," the American wrote on Twitter.