The debate between First Minister Alex Salmond and Better Together leader Alistair Darling was not broadcast to TV viewers in England, Wales or Northern Ireland, and those living outside of the STV region were advised to watch it through the broadcaster's website.
But many complained that the stream failed and STV admitted at the start of the broadcast that it was "having problems with the STV Player" and was "working hard to fix it".
Nearly half an hour later the broadcaster said it was still working on fixing the stream and advised the debate would be available online a few hours after the programme had finished.
BBC presenter Andrew Neil tweeted: "The one night rest of UK WANTS to watch STV and their systems freeze. Useless. Feed from STV making a great debate impossible to watch. Really angry."
The decision by ITV Borders, which is screened in the Borders region instead of STV, to stay with scheduled programmes on Sky and cable instead of switching to the debate was also criticised.
Viewers in the Borders were told they could watch the debate on Freeview instead, while the ITV channel showed Alan Titchmarsh's Love Your Garden and Behind Bars, a documentary about some of America's most dangerous young offenders.