Derby captain Richard Keogh has been ruled out until the end of the season after suffering a knee injury in a car crash following a team bonding session.
The Rams have revealed Republic of Ireland defender Keogh was among those who continued drinking after a team-building dinner with staff on Tuesday evening.
"As a club, we cannot, and do not, condone the actions of a small group of players on Tuesday evening," Derby said in a statement.
"The players were out as part of a scheduled team-building dinner with staff and while the majority of them acted responsibly and left at around 8pm and were not involved, a small group, including the team captain Richard Keogh, continued drinking into the night.
"They should have known when to stop and also ignored the opportunity to be driven home using cars laid on by the club, and chose to stay out.
"As a result of an alcohol-related incident, Richard Keogh has sustained a serious knee injury that will prevent him from playing until the end of the season."
Lawrence and Bennett were charged with drink-driving after a crash involving a Range Rover Sport and a Mercedes shortly before midnight on Tuesday.
Derby's statement continued: "The players involved in the incident on Tuesday evening will be subject to a rigorous internal investigation under the club's code of conduct and disciplinary procedures.
"But over and above any punishment they receive we will be expecting them to become involved with the excellent work the Community Trust does helping the communities we serve.
"We have been very clear about our attitude towards alcohol and the players know that at certain and specific times of the season they are permitted a drink together as a group in a controlled environment.
"Those involved in Tuesday's incident know they will pay a heavy price for their actions, but also that we will support them with their rehabilitation back into the squad and team.
"We fully support the work of our partners at Drinkaware and the unsanctioned actions of this small group of players is totally at odds with the stance that both Drinkaware and Derby County Football Club take regards alcohol.
"We will be using this situation to redouble our efforts in highlighting the dangers posed by alcohol.
"We would also like to thank the emergency services for their swift help."