An updated message said the qualifying session was now available to view.
Spark Sport purchased the Formula One rights after it had been shown regularly shown on Sky Television. It's the first big test for Spark ahead of the Rugby World Cup later this year.
The opening race of the season in Melbourne was also aired on TVNZ's Duke channel however the Bahrain Grand Prix, which takes place tonight, is the first race to be exclusively on Spark Sport.
"I feel like I need to thank you for actually doing your job," one comment responded on Facebook.
"I suggest your 1 month free trial should not start until you have a working platform," said another fan.
"Very frustrating, was really keen to get up this morning watch the qualifying and stay off social media to not know the results, too late... so annoying, think you need to extend your free trial until you can actually offer what you say you are offering," another comment said.
"For God's sake show F1 & F2 on Duke tonight. You may have the rights but that implies a responsibility to show the racing," wrote another frustrated viewer.
On the track, Ferrari driver Charles Leclerc topped all three sections of qualifying, to take his first pole position of his career.
"The car was amazing," Leclerc said. "A lot of emotions, I'm trying to stay as cool as possible."
Ferrari secured a 1-2 on the grid as four-time Formula One champion Sebastian Vettel qualified in second place.
Lewis Hamilton was third, followed by Mercedes teammate Valtteri Bottas. Red Bull's Max Verstappen qualified fifth followed by Haas driver Kevin Magnussen.