Normally any party should secure itself by carrying out the acts simultaneously as much as possible.
You should not have vacated the premises and handed over possession if you did not receive the deposit back.
At the least you should have taken a post dated cheque, though that also requires you to file a case under section 138 of the Negotiable Instruments Act but it is much quicker. Best is to take the Demand draft when you handover the possession.
If the landlord were to repay you by writing a letter, he would have done so even on your oral request. Be ready to fight for your money if the other party's intention is different.