Had Saints left Lambert and Shaw out, no doubt it would have led to speculation that they would be sold this month as they would not be cup tied.
Both players have been linked with moves away – Lambert to West Ham, not that it matters much now if he is cup tied! – but Mauricio Pochettino has always swept aside such speculation.
It would also have been easy to bring keeper Paolo Gazzaniga back into the fold against Championship opponents, but Saints kept faith with their most experienced available shot-stopper in Kelvin Davis.
In all, there were six starters against Burnley who had started against Chelsea three days earlier.
Aston Villa boss Paul Lambert – roundly criticised for his radio interview comments about the Cup being a ‘distraction’ – actually made fewer changes, just four, than Pochettino did.
But Villa were still on the receiving end of a major upset, losing at home to two divisions lower Sheffield United.
Blades goalscorer Jamie Murphy was fully aware of the old FA Cup magic. “These are the days that you play for ... it is one for us to remember.”
He is right.
When Saints fans think of Bobby Stokes, they don’t think of his 216 league appearances for the club, do they?
Same with Brett Ormerod. Mention his name and you think of the semi-final goal he scored against Watford in 2002.
Elsewhere, Fulham and Norwich made 17 changes between them for their clash. Fulham boss Rene Meulensteen gave debuts to four players, including 18-year-old French midfielder Ange Freddy Plumain and 19-year-old Lasse Vigen Christensen.
Canaries boss Chris Hughton also blooded two teenagers in the shape of identical 18-year-old twins Josh and Jacob Murphy.
Meulensteen said: “The FA Cup ... it gives you opportunities to bring other people into the fold. Four players made their debuts, four young players, which in my opinion is the biggest bonus.”
Saints had two teens on the bench who had been handed League Cup action earlier in the season, Sam Gallagher and Harrison Reed.
But with Burnley staging a late fightback, they were kept in reserve.
Pochettino got his team selection just about right, not that he will have been happy with all aspects of the performance.
He has to keep some of his fringe players as match fit as possible, hence Maya Yoshida and Jos Hooiveld playing together in the centre of defence.
Neither of those have had too many league opportunities this season, and have failed to really impress when their chances have come.
So it was the same at the weekend, a lower division club fighting back from 0-2 down to level and then grabbing a third late on to spark a nervous finale.
Pochettino will not have been happy with his side conceding three goals at home for the fourth time in the last five St Mary’s games.
Reed and Gallagher were in the right place on Saturday, on the bench gaining experience from just watching.
Pochettino was right to play them in the League Cup, but this competition demands more respect.
As I wrote in the Echo on Saturday, Saints have not yet grown too big to treat the FA Cup with disdain.
They could easily go on a long – and memorable – run this season, if handed some luck with the draws and they keep fielding very competitive teams.
Jay Rodriguez, for one, said as much at the weekend. “Every player in there wants to go as far as we can in the FA Cup,” said the striker after becoming the first Saint to hit double figures in terms of goals this season.
“It is a big cup for us and we want to get a good cup run going.”
That’s the spirit, Jay!
For a variety of reasons, none of them played against Burnley.
But, if fit, should all be considered for a run-out in the fourth round.
Saints again had the luck of the draw previously mentioned when they were pulled out at home to a Yeovil side struggling in the Championship.
The Glovers cannot be under-estimated, but Saints have a great chance to win through to the last 16.
Another decent draw and the fans who remember 1976 and 2003 with such affection will dream again ...