Wes Morgan scored the only goal of the game as Leicester beat Southampton on Sunday to move seven points clear at the top of the table, and Simpson believes his side showed their spirit in the narrow win.
Four more victories would secure glory for Claudio Ranieri's side and Simpson pinpointed captain Morgan as a driving force in their remarkable campaign.
"Wes does feel like a big brother. We are so close it is like your second family," he told the Mirror.
"You will probably see how we were at the full-time whistle, we knew it was a big moment.
"Every single one of us is giving 100 per cent for each other and the fans. We just have to keep going and keep knocking the games off."
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Simpson joined Leicester in August 2014, but was used sparingly in his first season at the King Power Stadium as the Foxes narrowly avoided relegation before establishing himself as a regular under Ranieri.
"It is hard work, determination, team spirit, good players, good manager , the fans, belief - every little thing put together," he added,
"It is unbelievable from where we were a year ago. But we will keep working hard and hopefully pick up some more wins."