"I'm very disappointed for the first half, and I'm the first to take fault for it, but in the second my players deserve credit".
Using his famed prowess in the air, the France global headed the Blues back into contention after Chelsea had gone 2-0 down at St Mary's and then, after Eden Hazard had made it 2-2, it was the boot of Giroud that secured a win that had looked unlikely for long periods of the game.
Giroud replaced the ineffectual Morata and, 10 minutes later, the France worldwide gave his side hope when he leapt to head Alonso's cross from deep for only his second goal for Chelsea since joining them from Arsenal in January.
"The most important thing is to never give up, believe in our quality, play our game and I am proud of what we have done today".
Southampton face Chelsea again in the FA Cup semi-final at Wembley next weekend.
Super Eagles forward Victor Moses was introduced for Eden Hazard with four minutes left in the game.
Third-from-bottom Southampton are five points from the safety zone after relegation rivals Crystal Palace beat Brighton & Hove Albion by the same score at Selhurst Park and Huddersfield Town beat Watford 1-0.
"But we have had the right spirit to come back and win this game". "It should have been a red card, clearly".
Burnley's run to the Europa League continued with a 2-1 win over Leicester, with Chris Wood scoring early on against his former club, turning home the rebound after Ashley Barnes' initial shot had been saved.
Bednarek marked his Premier League debut in style when he half-volleyed expertly across the goal and into the far corner from Ward-Prowse's free-kick on the hour mark.
Chelsea: Thibaut Courtois 6, Cesar Azpilicueta 6, Gary Cahill (capt) 6, Andreas Christensen 7, Davide Zappacosta 6, Cesc Fabregas 7, N'Golo Kante 7, Marcos Alonso 6, Willian 7, Eden Hazard 7, Alvaro Morata 6. In the 70th minute, Olivier Giroud made his mark, getting on the end of Alonso's cross and guiding his header into the bottom corner.