Goals from youngsters Dexter Blackstock and Nathan Dyer as well as substitute Brett Ormerod put the Saints in the second round.
Redknapp was heartened by his team's display, saying: "I thought we deserved to win - but not by that margin.
"In all honesty Southend passed the ball better than us. I was not totally happy with our passing or the ability of players to hold on to it.
"But the important thing is that we have kept our run going. This was our third victory in the space of a week, and I've got to be happy with that."
Redknapp was also satisfied with the way Blackstock and then Dyer virtually sealed the tie in the space of a couple of minutes just before the break.
Blackstock stabbed the ball into the net after goalkeeper Darryl Flahavan failed to hold on to a header from Matthew Mills.
Then the goalkeeper spilled a drive from David Prutton which resulted in 17-year-old Nathan Dyer marking his debut with a simple tap-in from a couple of yards out.
Southampton's final goal arrived in the last minute when Ormerod deflected a drive from Rory Delap.
"We paid the penalty for a couple of sloppy moments just before the break," said Southend manager Steven Tilson.
"You simply cannot afford to make mistakes against a quality side. You are always likely to get punished.
"Yet in the opening 25 minutes I was beginning to think we could get the result we wanted. We played some fine stuff during that time and caused them several anxious moments.
"But once they killed us off with those two goals just before the interval, it was all over. They killed the game in the second half and never allowed us to get back into it."Reuse content