The Foxes were flying ahead of the World Cup break following a difficult start to the season, only to suffer three successive Premier League defeats since the restart.
Saturday's 1-0 third-round victory at the English Football League's bottom club halted the slump ahead of a more high-profile cup clash at St James' Park.
Manager Rodgers is optimistic the slender success in Kent, sealed by the 16th FA Cup goal of Kelechi Iheanacho's career, can help his side regain momentum.
"That would be nice," he said. "It is well documented we didn't start the season well at all.
"We were able to turn it around and people were asking me would the World Cup would affect it and to be honest I didn't know.
"It's one where we weren't sure how it would go afterwards. We hoped we would keep that fluidity.
"We are missing a couple of important players and players who really make a difference within our structure.
"But days like Saturday, it is a good feeling to get the win, tough conditions, cold. And hopefully we can get the good feeling into our next game which is the quarter-final."
Creative midfielder Maddison has provided seven goals and four assists in the top flight this term.
But he is yet to feature for the Foxes since returning from Qatar due to a knee injury, having failed to play a minute during England's run to the World Cup quarter-finals.
Asked if the 26-year-old will be available against the Magpies in midweek, Rodgers said: "I don't think so.
"It's just day by day with James. Listen, we may go in tomorrow and it may be different but we'll see."