Martinez was in the stands at Anfield on Saturday as the Reds produced a faltering first-half performance against Villa.
Rodgers' side trailed 2-0 after 36 minutes, but fought back and grabbed a draw through goals from Daniel Sturridge and Steven Gerrard.
Despite the lacklustre showing, Rodgers said: "(Martinez) will know how I work and knows how my teams work.
"But he will know it will be a totally different game here for the derby.
"It wasn't one of our better days (against Villa), but we've had many great games here."
With Liverpool tackling Everton at Anfield on 28 January, Rodgers added: "We'll be ready for the derby game for sure."