Southampton's first participation in this competition may illustrate just how far they have fallen since their top-flight days, but 44,000 supporters made the trip from the south coast to see the 2003 FA Cup finalists take on their League One rivals.
The 10-point penalty for going into administration has left Saints off the play-off pace and they are just one spot above Carlisle - but the teams are leagues apart in every other sense.
Peter Murphy handed them the lead, literally, in the 15th minute when he stuck out an arm to whip the ball from the head of Lambert.
The defender was fortunate to escape with a booking but Lambert exacted revenge from the penalty spot with his 32nd goal of a prolific season.
Carlisle had their moments in the first half, not least when Matty Robson's cross was headed onto the top of the crossbar by Ian Harte.
However, it was Southampton who grabbed a second goal two minutes before half-time. Lambert flicked on Antonio's long throw and Lallana was left with the simple task of nodding the ball past Adam Collin.
Any hopes of a Cumbrian comeback were crushed four minutes into the second half when Evan Horwood made a hash of Lambert's cross. Collin managed to keep out Antonio's shot but Senegalese striker Waigo was on hand to nod the rebound into an empty net.
On-loan Reading winger Antonio crashed in the fourth from the edge of the area on the hour, before Carlisle substitute Gary Madine gave the blue half of Wembley something to cheer with a late header.