Goalkeeper Lenny Pidgeley and forward Gary Madine have been arrested in the past week for drink-related offences.
Cumbrians striker Madine was fined for being drunk and disorderly last weekend, while Pidgeley has been charged with drink-driving after being arrested last Sunday.
As a result, Abbott has moved quickly to lay down the law to his charges.
"They now know what I will and will not accept at this football club," Abbott told BBC Radio Cumbria.
"If they step out of line then they will be in serious trouble. We've had a meeting with the squad and I've said in no uncertain terms what I demand from my squad.
"As football players we have a certain responsibility to conduct ourselves in the proper manner and we haven't done that over this past week."