Can you wait until the next FY? No. If the asset was put to use in the current financial year, the depreciation is deemed to have been allowed for that year.
What if I didn't use it? If the asset was purchased but not put to use at all during the financial year, you cannot claim depreciation for that year. You would then begin claiming it in the year it is first put to use.
What if I have no profits? If you have no profits or a loss, the depreciation is categorized as "Unabsorbed Depreciation." You can carry this forward and set it off against other heads of income (except salary) in future years, without any time limit.