Chelsea were held to their third consecutive goalless draw in all competitions by Leicester, who were reduced to 10-men after 68 minutes.
On Friday Conte had described Leicester as the "worst team" his worn out group of players could come up against this weekend, following their midweek Carabao Cup semi-final first leg, and Foxes boss Claude Puel was left ruing a missed opportunity to take all three points off the defending champions.
He said: "I have another year of (my) contract with this club".
"We played with tiredness today", Conte said. "I think a lot of our players were exhausted".
"The ambition is not just for us to score but to continue to play after scoring and to always keep good ambition in our play".
GETTY Antonio Conte felt Chelsea's game with Arsenal on Wednesday made them tired against Leicester
James Ward-Prowse scored with two precise first-half finishes to put Saints in control before Andre Gray gave the home fans hope with a header early in the second half. The Belgian is the one who everyone connected to Chelsea turns to when they are need of a goal.
Chelsea also created a few chances of their own, but they failed to punish the away side's profligacy.
Conte says our attacking struggles are down to the whole team and not any one individual.
Watford v Southampton - Southampton are slipping towards the relegation zone off the back of a nine-match winless run and we can see Watford adding to the woes of Mauricio Pellegrino, who heads the sack race betting now.
Speaking to BBC Sport, Lawrenson said: "I was at the FA Cup tie between Fleetwood and Leicester on Saturday and Claude Puel's side did not play well, but he had made a lot of changes so you can not read too much into that performance".
Watford had trailed until Doucoure got on the end of substitute Troy Deeney's flick on and diverted the ball into the net past Southampton goalkeeper Alex McCarthy, with the ball appearing to come off his arm. This is not the Conte that we all know and adore - it's nearly as though he's thrown in the towel.
Premier League predictions: Can Liverpool halt the Man City juggernaut? I never see this type of mistake in the Premier League before.