Hodgson's England side were the first to be put out of the World Cup at the group stages since 1958, and many questioned if the former Fulham manager should remain at the helm.
However, FA chairman Greg Dyke was quick to confirm Hodgson's job was safe, and that meant a lot to the 66-year-old.
"I am very pleased of course that Greg and the board have come out and backed me to continue," Hodgson told Sky Sports News.
"We are midway through a term, there's lot of work to be done, but I also think we are on a good path.
"I can see a lot of possibilities for this team and these players to improve and become better and I am very pleased I am going to be the man leading them."
England will play their final World Cup match against Costa Rica in Belo Horizonte on Tuesday.