Aims: We have analyzed low frequency radio data of tidal disruption event (TDE) Swift J1644+57 to search for a counterpart. We consider how brief transient signals (on the order of seconds or minutes) originating from this location would appear in our data. We also consider how automatic radio frequency interference (RFI) flagging at radio telescope observatories might affect these and other transient observations in the future, particularly with brief transients of a few seconds duration. Methods: We observed the field in the low-frequency regime at 149 MHz with data obtained over several months with the Low Frequency Array (LOFAR). We also present simulations where a brief transient is injected into the data in order to see how it would appear in our measurement sets, and how it would be affected by RFI flagging. Finally, both based on simulation work and the weighted average of the observed background over the course of the individual observations, we present the possibility of brief radio transients in the data. Results: Our observations of Swift J1644+57 yielded no detection of the source and a peak flux density at this position of 24.7 $pm$ 8.9 mJy. Our upper limit on the transient rate of the snapshot surface density in this field at sensitivities < 0.5 Jy is $rho < 2.2 times10^{-2}$ deg$^{-2}$. We also conclude that we did not observe any brief transient signals originating specifically from the Swift J1644+57 source itself, and searches for such transients are severely limited by automatic RFI flagging algorithms which flag transients of less than 2 minutes duration. As such, careful consideration of RFI flagging techniques must occur when searching for transient signals.
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