Southampton McCarthy's closer denied Aaron Lennon and Jeff Hendrick, as Burnley enjoyed the best performance of the first half.
The hosts improved after the break when they brought in Danny Ings, but the new boy could not score with a header later.
FULL REPORT TO FOLLOW
Southampton vs. Burnley from the baseline
Southampton: McCarthy, Cedric, Stephens, Vestergaard, Hoedt, Bertrand, Romeu, Lemina, Armstrong, Redmond, Austin
Burnley: Hart, Lowton, Tarkowski, Mee, Ward, Gudmundsson, Westwood, Cork, Lennon, Hendrick, Wood