Regan was involved in an altercation with goal-keeper Mark Birighitti during training at Ray Watt Oval on Monday.
While it's not known exactly what spared the flare-up, it left Regan with a nasty split above his left eye.
"You want your players to have a competitive nature and show passion on the field because that's a key ingredient for success in any sport," Middleby said.
"However, it's important they don't cross the line and let their emotions get the better of them.
"As a club, we've spoken to both Mark and Taylor about the incident and have dealt with the matter internally."
While the Jets have ensured a rather difficult A-League campaign, it's a surprise this sort of incident comes on the back of a two-game winning streak that has breathed life into their finals hopes.
They sit just one-point behind the Central Coast who are in sixth spot ahead of this weekend's F3 derby at Bluetongue Stadium.
