The 50-year-old Russian appeared stunned in the spotlight of state television, describing how he had driven the train through to the next station despite smoke from a blast in one of its carriages.
"I followed the instructions," Kaverin said. "We have already had explosions and smart people developed smart instructions."
"At that moment there was no time to be afraid, it was time to work," he added.
Kaverin said he had learned that in such situations, he needed to drive the train all the way to the next station.
Russian investigators on Monday said Kaverin had made the "right decision" by not stopping the train between two stations, which enabled quick evacuation of injured passengers.
The head of Saint Petersburg's metro, Vladimir Garyugin, said that Kaverin had been a "hero."
"In emergency situations people become heroes," Garyugin said of the driver. "It would have complicated the (evacuation) task to carry people out" of the tunnel, he added.
Kaverin, who has worked at the Saint Petersburg metro for 15 years, will be rewarded for his actions, along with another unnamed employee who discovered a second bomb and called in experts to defuse it, said Garegin.
Kaverin, a father of two young children, said that he called his family to say he was alright as soon as he had the chance but was not able to return home on Monday night because of a mob of reporters waiting for him on his doorstep.
"It was a difficult day yesterday," Kaverin said.
He "quickly cordoned off the area and called in experts," thwarting another attack, Garyugin said.
Garyugin praised passengers for having remained calm and assisting one another during the evacuation.
"Both metro staff and passengers helped out one another," he said. "There were groans but there was no hysteria."
Saint Petersburg residents have also reported being offered free rides by willing drivers Monday night and the city's ground transportation was free for commuters.
The Saint Petersburg metro has since reopened, with authorities stepping up security on the city's busy underground transport system.
Russian investigators have launched a probe into an "act of terror" and said Tuesday that they believe they found remains of a suicide bomber inside one of the carriages.
Kyrgyzstan security services said Tuesday the attack was staged by a "suicide bomber" named Akbarjon Djalilov, a naturalised Russian citizen born in southern Kyrgyzstan in 1995.
Russian authorities have not commented on the alleged bomber's identity and it was not clear whether he counted among the 14 dead.