The Hoops skipper is of the opinion that there are too many observers who do not see beyond Lennon's passionate pitchside manner and appreciate that he has a firm grasp on the finer side of the game.
Lennon himself has spoken at length of how many people thought he was little more than a "rabble-rouser" when he was first brought into the Celtic dressing-room on coaching duty by Gordon Strachan.
Like the Scotsman before him, Lennon has taken the Parkhead side into the latter stages of the Champions League, an achievement that eluded his mentor, Martin O'Neill.
It is a considerable feat and one that Brown believes will have caused many to sit up and take notice.
The danger is that it is not just the players who may fall prey to wandering eyes. While the likes of Victor Wanyama, Adam Matthews, Joe Ledley and Gary Hooper may be attracting attention, Lennon will not have gone unnoticed.
Brown was fulsome in his praise of the Hoops manager and believes that if he stays at Celtic and keeps his current squad together, there is no limit to what the club can achieve.
"If you look at the amount of money he has spent you can see just what an achievement it is to go further on in the Champions League," said the midfielder.
"No other team in Britain has spent less than we have and then got through to qualify for the last 16.
"It just shows you the team that he is building here and the work that is going on.
"He is very good at going out and bringing in a player that no-one has heard of before and before you know it they look like players who are worth £10million.
"Look at Victor; nobody had heard anything about him before he came to Celtic and yet he is a player who looks as though he would be comfortable playing on any stage.
"It is phenomenal what the gaffer is doing and the way that he goes about his job.
"Whoever has been a critic of him doesn't know too much about the work he does."
Brown has also urged people to look beyond the figure that Lennon cuts on the sidelines on a match day.
Lennon has matured into the Celtic managerial role over the last few months, some of the pressure perhaps released by winning his first SPL title in May.
He has kept himself out of trouble this term, although he was involved in a spat with one of his own fans a few weeks back as Celtic toiled against Inverness Caledonian Thistle.
"I don't think he gets all the credit he deserves," said Brown. "People don't like his fiery character but that is what makes Neil, Neil.
"There is much more to him than that. He speaks very well, be that to the press or to the players.
"He knows what he's talking about and I think you only have to be in his company for a very short team to appreciate that. He is very articulate and good at getting his point across."
THE Celtic captain added: "He can get angry and frustrated, of course he can, but he is also a manager who knows how to get the best out of his players.
"Getting through to the last 16 of the Champions League should tell you that; it isn't something that is easy to do, especially when you consider the teams that we had in our group and how we were written off long before a ball had even been kicked."
The glamour of Europe's top competition will feel a long way off this week for Lennon and his players as they head to Arbroath tonight for a replay in the William Hill Scottish Cup.
The appeal does not carry the same pull as a Champions League tie, yet Brown insists the Hoops are approaching it with as much enthusiasm as they possibly can.
Brown himself may well be rested as Celtic try to coax him through his hip problem – an injury that the player himself has declared himself "bored" talking about. But the skipper won't be volunteering himself for a night off.
"Every game is a different game," he said. "Everyone wants to play and we want to enjoy it.
"Over the winter the pitches aren't always the best but I think we have players who are capable of coping with that and still getting the results.
"It may need to be a different style of football tonight and I suspect the conditions might not be the best, but we're looking forward to it and we'll just get on with it.
"When you're winning and enjoying your football, then everyone wants to play. You always want to go out and be involved and I think if you asked all the players in the dressing-room they'd all be as keen to play in as they would any other game."