Things I would need to know in order to do the calculation:
Current (i) drawn by the 3.3V load?
Drop-Out Voltage spec (Vdo) for your 3.3V regulator.
Open Circuit voltage (Voc) out of your DC adapter if you hang a big capacitor (~1000uF) across its output?
Does your adapter have full-wave or half-wave rectification?
Line frequency, 50 or 60Hz?
After you determine the answers, we will apply this formula:
C*ΔV = q = i * Δt, rearrange to:
C = i * Δt/ΔV
where C is the required input filter capacitor ahead of the regulator.
i is the load current in A.
Δt is either 8.33ms or 10ms, if 60Hz or 50Hz, full wave rectification. Double these for half-wave.
ΔV = Voc-Vdo