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."
The return of Stevan Jovetic meant City were at least able to field a recognised striker in the win against Sunderland, having deployed James Milner in that role due to limited options in recent weeks.
However, they are still without key players Edin Dzeko, Sergio Aguero and captain Vincent Kompany.
Dzeko and Aguero will definitely remain sidelined with calf and knee issues respectively, with Kompany - who has been troubled by a hamstring complaint - closer to a return.
Sheffield Wednesday have won the FA Cup three times in their history, although the last triumph came in 1935.
They reached the fifth round last year before a 2-1 home defeat to Charlton Athletic denied them a sixth-round clash with city rivals and ultimate semi-finalists Sheffield United.
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.
