The incident occurred in the first half of Celtic’s 3-1 victory at Tynecastle, which was broadcast live on BT Sport.
Naismith, on loan at Hearts from Norwich City, went to close down Brown as the midfielder looked to stop the ball from going out of play.
Naismith appeared to leave his boot in, standing on Brown as his opponent slid across the turf. He was also lucky to get away with a challenge on James Forrest, which saw him go into the ankle of the Celtic winger.
The Hearts attacker appeared to protest his innocence to Brown as the two had a bit of verbal sparring after the incident.
However, ex-Celtic striker Sutton was in no doubt that the foul was intentional.
He said at half-time: “Naismith should have been red carded twice in the first half.
“If he showed that intent at Norwich he might have got a game. Coward.”