Loss in rent due to old tenant moving out late -- deduct from security deposit?

[Dan Mitchell]

We had a tenant who decided unilaterally to move out two weeks later than the contractual end date. Consequently, the house could not be made ready for the new tenants and after a big scramble, we managed to save the new tenants but lost 3 weeks of rent. 

Can the 3 weeks in lost rent be taken out of the old tenant's security deposit or would we need to seek for those damages separately in court?

Thanks!