Whether it's fitness concerns or a tactical decision which leads to Conte's tendency to remove Hazard from the fray, supporters are unhappy that their best player isn't being allowed to help the side when they're chasing a goal.
Pushing their hosts with Vardy and Mahrez, the Foxes were a constant threat on Chelsea's back line and had the best of the chances in the first half.
Leicester have lost 12 of the last 14 meetings in all competitions, with the only exceptions coming during their title-winning 2015-16 season when they won at home and drew away.
Earlier this week Antonio Conte reiterated his commitment to Chelsea as he insisted he will not walk away from the club at the end of the season.
"For sure, everyone is frustrated after another 0-0", said Conte.
"I think he is with the doctor now, but it's OK, I do not think it was serious".
When looking to the bench, Conte did not have the players required to change the game as Morata once again struggled.
"When I chose to put fresh energy on with Willian and Pedro, the game changed".
Many of the Chelsea faithful, however, are losing faith in the Italian.
Leicester's relentless pressing made it hard for the Blues to create opportunities, even after they were reduced to 10 men following the second yellow card shown to Ben Chilwell. "We have to try to improve on this aspect".
Chelsea then left Wilfred Ndidi completely unmarked at a corner, but the midfielder's header was well saved by goalkeeper Thibaut Courtois.
Abdoulaye Doucoure's controversial last-gasp equaliser denied Southampton a first win in 10 matches.
Chelsea had seven shots on target in this match - only twice since 2003/04 have they had more in a Premier League home game in which they failed to score (9 vs Newcastle in November 2008 and West Ham in January 2014).