Celtic had the better of Sunday's Scottish Premier League clash but were struggling to make the breakthrough until Maloney fell inside the box under pursuit from Steven Saunders to allow Daryl Murphy to net a 73rd-minute winner.
Dougie McDonald sent off the Motherwell right-back and, although Brown felt the teenager should have held off from making the challenge, he thought both Maloney and referee were quick to act.
He said: "I think it was easy to give. It's a through ball, two players are running for possession. There is a challenge from Steven Saunders on Shaun Maloney but his legs quickly left the ground, when you see it on TV.
"Dougie McDonald is not in the best position, there are a couple of players in between him and the incident, but he was very quick to give it so we have got to accept that.
"There is bodily contact there, I saw that, but Maloney went down very, very easily.
"He went down very softly but I'm not wanting to talk about a player from another team. I'm faulting our own player for giving the referee an opportunity to give the penalty."
Brown added: "When a player, especially an Old Firm player, is going into the box, he is going away from goal and is on his weaker side, you don't need to make a challenge. Just run alongside him and let him make the keeper make a save.
"It would have been difficult to score from where Shaun Maloney was.
"But Saunders is an outstanding player, he will be top class, in fact he is already. He is in the (Scotland) under-21 squad when he's still eligible for the under-19s.
"He will learn from it but we lost a couple of points that we might have had."
However, Brown admitted his side had been second best after their exertions on Thursday night when they did everything but score in a 1-0 Europa League defeat by Odense.
Brown, who lost Stevie Hammell to a hamstring injury and Steve Jennings to illness during the game, said: "Celtic were marginally the better team and deserved to win the game, although we could have shared the points.
"But it was the poorest we have been this season and I attribute that to nine games we have had with the same group of players."
Celtic were able to make five changes following their 4-0 Europa League defeat by Utrecht with Fraser Forster and Emilio Izaguirre making their debuts.
On-loan Newcastle goalkeeper Forster had little to do but Izaguirre looked agile in defence and attack, leading Brown to compare him to former Brazil left-back Roberto Carlos.
Celtic first-team coach Alan Thompson revealed that Celtic hoped to make two more signings before the transfer window closes on Tuesday night.
Celtic have been linked with moves for striker Itay Shechter, although Hapoel Tel Aviv are unlikely to sell after reaching the Champions League Group stages, and Hibernian forward Anthony Stokes.
Thompson also revealed that some video sessions had prepared the players for their high-pressure afternoon in Lanarkshire.
Thompson, who replaced manager Neil Lennon at the post-match media conference, said: "We got them in on Friday and everyone got bits off their chest.
"We first sat down and watched the game as coaches and then everyone together.
"Some of the boys knew what they were coming into today because they have been in Scotland for a while. For some boys it was new ground but they coped well.
"We sat down last night and showed the new boys a lot of clips of Motherwell, just to give them a heads-up."
Thompson added: "Let's not get away from it, we are disappointed not to be in Europe but we can't fault them domestically."