Around 5,000 Foxes fans travelled along the M69 on Saturday for the Championship clash against Midlands rivals Coventry at the Ricoh Arena.
Brown has been impressed by the level of support since his arrival from Hull in January 2008.
"It's great to look behind the goal and see our support fill up the whole end of a stadium," Brown told Leicester's official website. "I know the lads appreciate it and we all recognise just how important the supporters are to our team.
"The supporters have been nothing short of fantastic since I joined the club and for nearly 5,000 of them to make the trip to Coventry, after nearly 1,000 went to Middlesbrough on a Tuesday night, is really something.
"We need the supporters behind us, as they have been last season and this season. Who knows what we can achieve together."