Lukaku scored twice in the first half - one of which was set up by Barkley - to put Everton in control at St Mary's. England midfielder Barkley then capped off the display with a fine third goal late on.
Speaking after the game Martinez was quick to praise the match-winning duo as well as giving special mention to Arouna Kone, who was also credited with an assist.
"They [Barkley and Lukaku] were unplayable.When we play to their strengths they are very, very special.
"To see the best qualities of an individual you need a good team performance, so it would be wrong to highlight individual players too much.
"Arouna Kone’s contribution helped Ross and Rom to have the space they need but overall the team was perfect."
"It wasn’t about the points, it was about the performance," insisted Martinez. "We made it a complete team performance. Every time we have come here, we have found it difficult but we had everything today; we had real flair and kept the ball well.
"We defended very cleverly and kept Southampton at bay.
"The way we started the game was pleasing. Tim Howard had to be at his best (before the first goal) but apart form that we were in control.
"You need to be flexible - if you are predictable it’s easy to stop. We were dynamic and powerful on the counter and we were difficult to stop on the ball as well. We got the right balance."
Barkley was quick to hail the team's performance at full-time, with a clean sheet a welcome bonus after they conceded two sloppy goals against Watford last weekend.
He told BT Sport:
"The lads showed a lot of confidence from the off. It's a credit to the backroom for getting us all together. The clean sheet is good for all the team. Gives us a lot of confidence. You know how good Lukaku can be. When he's playing like that he is the best in the league."