Barkley immediately stepped up to take the kick despite the presence of regular takers Jorginho and Willian on the pitch, with the latter in particular appearing to protest his call.
Frank Lampard said after the game that Barkley is a designated taker, but there was a clear disagreement between the players on the pitch.
“It’s almost disrespectful to your team-mates to do something like what Ross Barkley did this evening,” Gudjohnsen said on BT Sport.
“I’m pretty sure it’s clear who is the penalty taker before the game.
“Just to create all the fuss, the tension between your team-mates and yourself and then go on to miss the penalty, you just put yourself under so much more pressure than actually just taking a penalty.”
Such penalty confusion appears to be developing as something of a theme this season, following a similar situation at Manchester United with Paul Pogba and Marcus Rashford both missing kicks during the opening weeks of the campaign.
But while Barkley appeared full of bravado as he placed the ball on the spot straight away, Gudjohnsen thinks Blues skipper Cesar Azpilicueta should have taken control of the situation.
“If you’re the manager in a situation like this,” he posed, “where you’ve got one, two, three, four players standing over the ball, and there is a question on who is going to take the penalty, don’t you want your captain to step in and say, ‘Listen, it’s been decided before the game who is the penalty taker’?
“Show that authority as the captain to make the decision for everyone who’s on the pitch.”