The home side were reduced to 10 men in the 58th minute when Brown was red carded by referee Stephane Lannoy after flicking a leg at the Barca forward following his original foul on the Brazilian star.
The Scottish champions were dealt another blow in the 76th minute when Cesc Fabregas headed the winner for the Catalans to leave the Scottish champions with no points from two Group H games.
Asked about his captain's red card, an unhappy Hoops boss said: "I think it is very soft. I have looked at it.
"If there was any contact, it was minimal. There was a lot more in a game that warranted heavier punishment.
"It was a game-changing decision. It is obviously very difficult playing Barcelona with 11 players and even more difficult with 10 but we played very well tonight.
"I don't think the initial tackle was a severe one. It is a physical game I don't think Neymar does himself any favours with the way he behaves at times.
"Our supporters are very respectful of great players. Iniesta walks off tonight to a standing ovation from the Celtic support. After the incident Neymar gets booed every time he touches the ball."
Asked if Brown should not have given the referee the opportunity to send him off, the former Celtic skipper said: "Possibly. It is a debatable point but again there wasn't much in it.
"There is no question it is a foul, but the reaction didn't merit it.
"The referee was going to book Scott for the initial foul but for the tap, if you want to call it that, he has sent him off. Is it violent play or dangerous play? I am not so sure.
"There was a lot of heavy challenges going on in the game. Was that a sending off? Not in my view."
Lennon lamented the two opportunities his side had just before Fabregas headed in from Alexis Sanchez's cross.
The Northern Irishman said: "We had two fantastic chances, Victor Valdes' save (from James Forrest) was amazing and Charlie Mulgrew should score (with a header).
"It was a great opportunity and then two minutes later Cesc scored the winner so the game hinged on those five minutes.
"We needed our keeper to make great saves at the end but that was almost academic.
"At 11 versus 11 I was really happy, especially in that spell after half-time. You are talking about the best club team in the world and they wear you down."
Barca boss Tata Martino played it with a straight bat when asked if Neymar overreacted at the Brown red card.
He said: "I couldn't see with certainty what happened so I don't want to give an opinion.
"But certainly playing with 10 men for 35 minutes against Barcelona is something to think about when analysing the game."
Martino was happy with the way his side went forward in the absence of Lionel Messi, who was missing through injury.
He said: "We obviously prefer to play with Messi but when he is unavailable his absence cannot be used as an excuse.
"We have some excellent players. This match was the most demanding so far, Victor Valdes made important saves for us."
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