Brendan Rodgers joined Leicester from Celtic in February 2019
The Foxes are bottom of the Premier League, having claimed one point from six games so far this season and face 17th-placed Aston Villa on Saturday,
Asked whether he has considered his position at the club, Rodgers said no.
The 49-year-old said: "I am not daft, I understand football, it has not been a great start at all."
"But the support shows the level of work we have done here and the appreciation of what we have been through over the course of the summer," added Rodgers. "It's been very supportive."
He said it is his "responsibility to improve the results", adding: "There is no question about that."
Leicester won the FA Cup in 2021, with Rodgers taking charge in February 2019 and his side finishing fifth later that season.
He has previously expressed frustration at Leicester's transfer dealings after the Foxes sold key defender Wesley Fofana to Chelsea for about £70m and brought in just two players - former Cardiff goalkeeper Alex Smithies on a free transfer and centre-back Wout Faes from Reims.
But Rodgers said he has "had nothing but support", explaining: "I love being here, my record here is concrete in terms of what we have done and how performances have been.
"But it has not been to the level [expected]. It is not easy when you are not getting results but it provides the motivation to get things right."
-- Courtesy of BBC Sport