Landlord charged me few days of rent, what is my right here?

[Joms Marfil]

Long version:

So I received the final statement from the landlord and I was surprised that they have charged/deducted me a couple of days rent after my move out date. I told them I will move out on June 30th and they asked me to leave the apartment on that day. I was informed that they have found a new tenant at least a month before June 30th and now they are saying the tenant just moved on July 9th and so I am responsible for the rent from July 1st-8th. 

Yes it was indicated on the lease contract that I will be responsible for the rent up to the duration of my lease but at least they should have informed me that the new tenant will move in on July 9th and so I could have stayed a little bit longer and enjoy the days of the rent that I will pay for and have done a graceful exit.

Short version:

Lease will expire on Aug 31st, I moved out June 30th.

New tenant moved in July 9th, they have deducted 8 days to my security deposit.

Do I have a legal claim here to get back my money? TIA