Thibaut Courtois was a shock inclusion in Chelsea's picks to take a spot-kick against Arsenal and he saw his attempt fly over the bar.
Alvaro Morata then dragged his penalty wide leaving Olivier Giroud to win the trophy for Arsenal.
Established players such as Victor Moses, Cesc Fabregas and David Luiz weren't included in the shoot-out but could have been lined up to take the final two.
But Owen insists he would never allow a goalkeeper to take a penalty ahead of him.
He tweeted: "If I were an outfield player and a GK took a penalty ahead of me I'd struggle to look myself in the mirror."
Antonio Conte has been vocal about his frustration at Chelsea's activity in the transfer window this summer.
Despite signing Tiemoue Bakayoko, Antonio Rudiger, Morata and Willy Caballero, the Chelsea boss reportedly wants four more signings to add to his squad.
The reigning Premier League champions have Champions League football to contend with this season.
And Owen went on to say he may have changed his pre-season prediction of Chelsea retaining their title after the performance against Arsenal.
"I thought Chelsea were the team to beat this season but today was worrying.
"Not often a team looks weaker after a summers transfer activity."
