Guardiola's men ran out 6-3 winners over their cross-city rivals thanks to two hat-tricks from Erling Haaland and Phil Foden.
Manchester United could not deal with the threat City posed in attack, and Guardiola saw a weakness in the Red Devils' backline.
The Spanish tactician reportedly instructed Phil Foden and Kevin De Bruyne to attack the space left by Martinez on the left-hand side of United's defense.
This was due to the Argentinian being expected to double up on the talismanic Haaland with Raphael Varane.
Guardiola's plan paid dividends as Haaland and Foden punished a poor United defense but not all the blame can be cast on Martinez.
The Argentinian centre-back is just the latest Premier League defender to struggle against City's formidable attack.
Haaland has already bagged 14 goals in just eight appearances this season whilst the likes of De Bruyne and Foden have been excelling too.
Jack Grealish also created havoc for Diogo Dalot on the right side of the Red Devils' defense on an afternoon to forget for Erik ten Hag's men.
City are currently second in the Premier League, winning six and drawing two of their opening eight fixtures.
Meanwhile, United sit sixth after the defeat to the Cityzens as they have won four and lost three league games.
Manchester United's Martinez bounced back against Omonia Nicosia
Manchester United required a second-half comeback to beat Cypriot minnows Omonia 3-2 in the UEFA Europa League on October 6.
A double from Marcus Rashford and an Anthony Martial strike canceled out Karim Ansarifard's first-half opener, while Nikolas Panayiotou's late effort gave United a nervy finish.
Martinez's performance in the win at the GPS Stadium was impressive as the former Ajax defender completed 90 passes with a success rate of 89%.
He won 100% of his aerial duals against Omonia and five of his eight ground duals.
It bodes well for United, who had been performing well defensively prior to their collapse at the Etihad Stadium. Martinez has forged an impressive partnership with Varane at the back and the duo are keeping captain Harry Maguire out of the team at the moment.
Next up for United is a trip to Goodison Park to face Everton on October 9 as they look to get back to winning ways in the league.