She said about 8500 passengers normally caught Auckland trains during the 4pm to 6pm travel peak.
Auckland rail operator Veolia ordered taxis for some stranded passengers.
Although KiwiRail restored some services within about an hour, passengers waiting at the downtown Britomart station were advised to use buses for the rest of the night while train services were reorganised.
Rail passenger Trixie Webber said she was new to Auckland and "wouldn't know how" to catch a bus home to Greenlane.
She and others were directed by loud-speaker announcements to replacement buses outside Britomart, but many commuters had difficulty understanding where they were supposed to go.
Only word-of-mouth notice was given of the first train to leave Britomart before 5pm, as electronic bulletin boards kept advising passengers that all services were suspended.
Long-time passenger Ronnie Patrawale heard too late that the train was going to his destination of Glen Innes, and faced an indefinite wait for another.
He said that although driving to Glen Innes from Howick and then catching the train remained more convenient than bringing his car all the way into Auckland, rail services had been patchy in recent weeks.
Daily rail commuter Alain Monks was resigned to catching a special-service double-decker bus from a stop tucked away behind Newmarket.
Such a disruption was rare, he said, and "you have to take it on the chin".
But Mayor Brown said the failure was disappointing at a time when hundreds of millions of dollars was being spent on upgrading Auckland's rail network and patronage was at record levels.
"KiwiRail has assured me they're taking this very seriously and a full investigation is under way into what went wrong," he said.
"It's clearly embarrassing for an issue in Wellington to bring Auckland trains to a standstill, and I know all the stops will be pulled to prevent a repeat."
KiwiRail chief executive Jim Quinn said the organisation was taking the failure very seriously, and had started an urgent investigation into the cause.
"We understand that at this critical time of day this will have caused widespread disruption and we do apologise sincerely for this."
KiwiRail is nearing completion of a $90 million upgrade to signals on Auckland's network in preparation for electrification next year.
Spokeswoman Jenni Austin said that although the organisation had yet to "understand" the exact cause, it was satisfied none of the communications or signalling equipment in the Wellington control centre was to blame.
The cause was a power cut within the building and the failure of a back-up system to kick in.
"This is likely to be a very specific issue that will need a close technical investigation," Ms Austin said.
Although KiwiRail had an alternative train-control facility in Auckland, it had been set up in case the Wellington centre was unable to operate for extended periods and was not staffed for an immediate switch-over.