"The first half wasn't good, not only from tactical aspect", the Italian told Sky Sports.
"I think the first half was very negative".
"We showed great character and team spirit". If they do, they will rue Saturday's game at St Mary's in which they were coasting at 2-0 until Olivier Giroud came on as a 61st-minute substitute.
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. If they decide we can't fight in the right way, I'm the first person to take responsibility.
Eden Hazard finished smartly to put Chelsea level minutes later, and Giroud would come up with the goods again, scoring the victor off his foot to hand the visiting Londoners a 3-2 win.
He said: "I think that the coach has to try to find a different solution, especially if you are losing, but I think the difference was that we played in the second half with great desire not to lose another game. No-one deserves this type of season".
However, Conte's opposite number Mark Hughes was unhappy that Alonso had escaped a red card and has called for the player to receive a retrospective ban ahead of next week's FA Cup semi-final between the two clubs.
And with Southampton reeling, Giroud completed Chelsea's comeback when he pounced on a loose ball inside the area to drive into the bottom corner.
"It's a really poor challenge", he insisted.
"I said when I came on we need to fight until the end, keep believing". I was very disappointed.
Chelsea were not much better immediately after the restart and, after failing to heed a warning courtesy of Shane Long, the Saints' lead was doubled thanks to a fine finish from Bednarek, who was making his first start for the club.