Brown received his second yellow card of a dramatic afternoon at Rugby Park after his deflected 90th minute shot earned Celtic a 1-0 victory over Kilmarnock and sparked wild celebrations among the visiting support.
Rodgers expressed his disapproval at the actions of some Celtic fans who invaded the pitch but was adamant referee Bobby Madden was wrong to punish Brown for his part in the scenes which greeted the goal.
“I always think that’s unfortunate for players,” said Rodgers. “Of course there’s the reaction from Scott going to the crowd. “But with it being at the end of the game and the emotion of it, I always think it’s harsh for a player to get sent off.
“I can’t blame Scott, I thought he was excellent in the game. He had good control. He had a challenge early on that he was booked for but I thought he was excellent. “It’s very hard for Scott or any other player, especially when you score late on. We don’t get so many late goals now - we normally have a comfort in the game - but to get a winner like that, so late, you want to go with your team-mates to your supporters. So to then get sent-off for it is always harsh.”
Celtic have now won their last six Premiership fixtures without conceding a goal. The victory at Kilmarnock ensured they took full advantage of closest title rivals Rangers’ dropping points in a goalless draw at home to St Johnstone on Saturday.
“Everyone talks about when rivals slip up and draw, as Aberdeen and Rangers did this weekend, but you’ve still got to exploit that,” added Rodgers.
“Obviously to come here, a very difficult place on the back of a really tough midweek game against Valencia in Europe, just keeps our domestic form going to a really high level.
“I thought we played well and had good control. It’s another step. There are still 12 games left to play, so still a lot to play for.”
Killie boss Clarke, who had no gripes with the straight red card shown to his defender Kirk Broadfoot for a foul on Brown with 15 minutes remaining, was understandably dismayed by the outcome.
“I thought we played well and certainly didn’t deserve the cruel break at the end,” said Clarke.
“Obviously when you go down to 10 men it is more difficult but even at 10 men I couldn’t see Celtic scoring.
“It took a big deflection off Alex Bruce to get the goal, we didn’t deserve that. The shot from Brown was going over the bar. I’m sad about the result, but not the performance.
“From the side of the pitch, it (Broadfoot’s challenge) didn’t look great, to be honest. I won’t be complaining too much about it, I don’t think, if there is contact.”
Asked about the scenes after Brown’s goal, Clarke replied: “You are always concerned when fans come on the pitch like that.
“In a sort of backhanded way, the celebrations were probably a little bit over the top and it is a big compliment to Kilmarnock that Celtic come here and celebrate a victory like that.”