The home side had one last chance in stoppage time when they had a free kick from 25 yards out, but Marcos Alonso sent the ball over the bar and the game ended in a 0-0 stalemate.
"I think we played with a lot of top players against Arsenal, and then again today against a very good team".
Antonio Conte says it is up to Chelsea whether he stays at the club or not.
He said: "I understand that the other teams try to kill (rival) teams and to anticipate the situation".
On Friday Conte had described Leicester as the "worst team" his tired 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. "I think a lot of our players were exhausted", Conte said during his post-match interview.
Leicester continued to put pressure on a sleeping Chelsea defence as the first half progressed, with Vardy finding it easy to burst through the Blues backline and into a risky area.
Chelsea really need to rediscover their spark against Leicester, with Morata especially in need of a boost. He has made just two league starts this term after being named in the first XI only once in 2016-17 - sparking talk of a possible loan switch to Sevilla.
Equally important, winning in fine style would also help re-balance Conte's state of mind and perhaps help him realise that settling his feud with Mourinho can be done on the pitch by his team playing a better brand of football and winning more trophies.
Meanwhile, Leicester striker Jamie Vardy is fit after recovering from a groin injury, according to his manager Claude Puel.
"It was a good game for us, we showed a lot of quality, we played well, but if it were 11 v 11 I think we would have got the win", he said.
Abdoulaye Doucoure's controversial last-gasp equaliser denied Southampton a first win in 10 matches, with the midfielder diverting the ball in with his arm a minute before fulltime as hosts Watford came from two goals down to snatch a 2-2 draw.