That response didn't arrive in the opening stages of the second half, with Shane Long going close yet again.
It remains to be seen if he would be tempted by a return to the Stamford Bridge, though the chance to prove himself in the Premier League again, should Chelsea be unable to land their other top targets, will nearly certainly give him plenty to deliberate.
Another tough test is on its way for Conte and his men as we prepare for the trip to high-flying Burnley on Thursday.
Chelsea are facing an uphill battle to finish in the Premier League's top four this season and will surely need to win at Turf Moor if they are to stand any chance of reeling in either Tottenham Hotspur or Liverpool.
Visiting inroads were few and far between beyond that in the first half, however, with Marcos Alonso lucky to avoid a yellow card for a clumsy challenge when seemingly standing on Shane Long's calf.More news: Nine-year-old girl raped in Surat, body found with 86 injuries
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"We didn't show great desire and great will to fight". Chelsea got a third goal from Eden Hazard, and went on to win 3-2. "If you don't have something in you're heart, it's hard to come back and win this game".
It was Conte's changes that turned the game in Chelsea's favour, with Giroud grabbing his first and second for the club, but the manager was more concerned with the difference in his team as a whole for Chelsea's first league comeback from two goals down since 2002.
Less than 10 minutes after coming off the bench just past the hour, Frenchman Giroud met Marcus Alonso's cross for his first goal.
"As has been the case all year apparently we've got a soft underbelly", said Saints boss Mark Hughes, whose three Premier League games in charge have now all ended in defeats. The most important thing is to always play with a great intensity, with a great will to fight from the start until the end.
Chelsea FC will return to FA Cup action next weekend when they take on Southampton in the semi-finals.
Chelsea's central defenders kept the ball alive inside the box from Hazard's cross, before Giroud's quick-shot half-volley put Chelsea into the lead.