Paul Cook was full of praise for his players after Wigan Athletic's FA Cup adventure came to a halt.
Having beaten Bournemouth, West Ham and Man City to secure a place in the quarter-finals, they couldn't add a fourth Premier League scalp to their haul.
Two second-half goals secured Bournemouth a 2-0 win at the DW Stadium.
It was a pulsating match in freezing conditions and afterwards, Cook told the BBC: "You can't ask any more, you want to come out of these games feeling you've done yourself proud and I thought first-half especially, we were excellent.
"We expected the reaction with the quality of players Southampton have got and we certainly wish them well in the semi-final."
Latics only trailed 1-0 - to Pierre-Emile Hojbjerg's 62nd minute strike - when man of the match Christian Walton pulled off a stunning penalty save to keep their hopes alive.
But Cedric Soares secured the result in injury time.
Southampton manager Mark Hughes, who was only appointed midweek, added: "Wigan were an absolute credit to their manager and their fans and I congratulate them on how hard they pushed us."