Former Arsenal striker, Giroud, headed in the first goal, and delivered a left-footed drive while Eden Hazard's shot equalized for the soon-to-be-deposed EPL champions.
One of those players - wing-back Marcos Alonso - was also fortunate to escape without punishment for standing on the back of Southampton forward Shane Long's calf in the first half.
The Germany international, 25, had been one of Chelsea's top performers before he was left out of Saturday's comeback victory, with Gary Cahill starting alongside Andreas Christensen and Cesar Azpilicueta.
"I think that was the first chance they have".
However, speaking after the match, Conte refused to comment on the tackle itself, claiming he did not see the incident.
Southampton's joy was short lived though as the Pensioners found the back of the net three times in the space of eight minutes to win the match 3-2 in the end.
Giroud came to the party big time and scored two goals to belatedly announce his arrival in style at Chelsea. If I can assist, I assist.
"After the first half I was very disappointed but I am the coach and if the desire is not right and we cannot fight in the right way, I am the first person to take responsibility".
"No [there is no injury], it was a tactical decision", Conte told reporters at St Mary's Stadium.
"I am at the best club in England in recent years because Chelsea have won more trophies than anyone else".
"We missed the first 25 minutes", said Tottenham manager Mauricio Pochettino, whose side face Manchester United in the FA Cup semi-finals next week.
Liverpool continued their scintillating run of form with a routine 3-0 win over Bournemouth with goals scored by the attacking trio of Mane, Salah and Firmino.
The club captain retained his place following the draw with the Hammers and showed typical passion and the sort of commitment and urgency that needs to be standard throughout the team. He had very little impact but was a different player as Chelsea fought back, setting up the equaliser with a great stepover and cross.
"I feel that we have done work that has helped the guys to understand what is required at this level and help with what's required but it's the key moments in games where you have to be resolute and clear your heads quicker than we are able to do at the moment and get something out of games you deserve to get something out of", reflected Hughes.
"I think in the second half we [could] finish the game [off]", Rudiger said last week.
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