City have reached the final of the competition twice in the past four seasons, beating Stoke City 1-0 in 2011 but succumbing to a shock defeat to Wigan Athletic two years later that ended Roberto Mancini's managerial reign at the Etihad Stadium.
Wigan - now a second-tier side - also dumped City out of last season's competition in the sixth round and the Premier League champions face another potential banana skin on Sunday when Wednesday - who sit 10th in the Championship - head to town.
Pellegrini's side are currently riding the crest of a wave, however, after a 3-2 victory over Sunderland on New Year's Day moved them level with Premier League leaders Chelsea.
And while defending their title will no doubt remain at the centre of the Chilean's thoughts, he is not about to let complacency seep in against Stuart Gray's side.
He said: "We have played three games in a week [over the festive period], three very important games.
"We have finished and now we must start thinking about Sheffield Wednesday and the FA Cup.
"For our team it is a very important cup. We are eliminated from the League Cup so we will continue in the FA Cup as far as we can.
"I am very happy with the way we are playing; we have so many injured players but we arrange it in different ways to continue winning."
Sunday's meeting is the second between the sides this season, with City having annihilated Wednesday 7-0 in September's League Cup clash.
Frank Lampard and Dzeko grabbed doubles that evening, their goals added to by Jesus Navas, Yaya, Toure and Jose Angel Pozo's maiden senior goal.
