Chelsea have closed the gap to 7 points on fourth placed Tottenham who have a game in hand.
It was only after Giroud's introduction in the 61st minute that Chelsea took charge, as the France worldwide scored twice either side of an emphatic Eden Hazard finish to wrap up an unlikely victory and leave Southampton languishing in the bottom three.
"I am disappointed in the first half, I am the first to take the fault for that, but in the second half my players deserved credit".
Following Southampton's earlier defeat Palace were 3-2 winners over Brighton, with all five goals inside the first half.
But Giroud's introduction off the bench in the 61st minute proved the catalyst for Chelsea's comeback, as he pulled one back soon after and then got the victor following Eden Hazard's equaliser. I have been through difficulties in my career, other times I tried to come back stronger.
"The most important thing is to show some character".
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Meanwhile, Southampton manager Mark Hughes was unhappy that Marcos Alonso had escaped a red card after a high boot caught Shane Long on the back of his calf at the end of the first half. We need to finish this season in the best possible way.
"Southampton played a good game and took a lot of confidence after their first goal because they were nervous at the start".
Conte also reserved special praise for two-goal hero Giroud. It was hard for us to come back so we must be pleased by the desire we showed.
If you don't have something in your heart, it's very hard to win the game, but today I'm very happy with the second half, and very disappointed with the first.
Conte was happy that his players showed "great heart" to comeback, but gave a frosty response about Rudiger's omission from the matchday squad.
And although Conte was impressed with the comeback - the first time Chelsea had come from two goals down to win a league game since 2002 - he was keen to ensure people knew his opinion of their first-half display.