The Hoops captain was red-carded in the 58th minute after flicking a leg out at Neymar following a foul on the Brazilian, before Cesc Fabregas scored the winner for the visitors.
Brown apologised to the players in the dressing room afterwards but was robustly defended by his boss in the post-match press conference and again, when the Northern Irishman spoke to Celtic TV.
Lennon said: "Looking at the incident again, I stand by what I said. Contact is minimal, if there is any at all.
"People might call it petulance but is it a sending off? No.
"The tackle by (Sergio) Busquets on (Beram) Kayal, that warranted a red card for me and Emilio Izaguirre on (Dani) Alves.
"There were far more physical and worse challenges in the game than Scott's and I feel aggrieved.
"I am getting criticised for that now and that's fine. It's my opinion, he's my captain.
"He has come out and apologised for it which I don't think he needed to do but maybe he felt compelled to do that for the supporters.
"But I am disappointed with the reaction of Neymar."
Lennon confirmed he would not be appealing the sending-off.
The former Celtic skipper said: "I would have if the ban had been more severe.
"But at the minute we are looking at a one-game ban, so we don't want to make things any worse."
- Sports & Recreation
- Cesc Fabregas