The result represented the third goalless draw for Chelsea in the space of a week following cup games against Arsenal and Norwich City and Conte thinks that his side's hectic schedule, which has seen them play 10 games in the last month, is partly to blame.
Claude Puel's Leicester lie 8th in the table after enjoying a decent start under the former Southampton manager.
Having played Arsenal in the Carabao Cup semi-finals on Wednesday evening, the home side struggled to get going and were fortunate not to be behind at half-time after Leicester created several good opportunities.
Leicester City have won just once in their 11 previous Premier League visits to Stamford Bridge (W1 D3 L7) - winning 2-0 in September 2000, with Muzzy Izzet and Stan Collymore getting on the scoresheet.
Conte substituted Eden Hazard and Cesc Fabregas for Pedro Rodriguez and Willian in the 58th minute and Chelsea took charge after Ben Chilwell was shown a second yellow card for catching Victor Moses on the ankle, but Leicester held on in relative comfort to earn a draw. The Red Devils have reportedly identified Vardy as one of the targets as a back-up for Romelu Lukaku, claims the Telegraph.
Conte has won 25 of his opening 30 home Premier League games as manager, no boss in the competition has won more of their opening 30.
Conte said it was normal for Chelsea's manager to face speculation about their position
With Manchester City dominating the top flight of English football this term (16 points above Conte's side), there has been some disturbance at Chelsea, who are the defending champions but are more or less out of the race to retain their title.
Since August 2014, Jamie Vardy has scored more Premier League goals against "big six" opposition than any other player (22 goals in 41 apps). "If you don't score, you're lucky the game finishes 0-0".
Antonio Conte says it is up to Chelsea whether he stays at the club or not.
There was a major injury concern for Chelsea as 33 minutes in club captain Gary Cahill pulled up with a hamstring injury after chasing down Vardy. "Me and the club know very well this situation and for this reason we must have patience to understand there is a process and we are ready to face this process".
Chelsea were camped on the edge of the Leicester box for long periods late on, trying to prise apart the disciplined 10 men in front of them.
Quake hits Iran-Iraq border region, felt in Baghdad
The epicentre, with a depth of 8km, was determined to be at 33.78 degrees latitude and 45.74 degrees longitude. The temblors hit on Thursday morning, were felt far and wide and even rattled the Iraqi capital of Baghdad.