Biggar was caught on broadcast microphones shouting “get the f*****g ball off” at North, as Wales flirted with danger deep in their own half.
Wales tiptoed home in a turbulent clash which saw both sides score four tries, but Fiji blew several fine opportunities to win the contest.
Asked about Biggar’s terse ticking-off, Gatland said: “I don’t have a problem with that. It is about making people accountable.
“There were times in the first half where we put the ball through the hands or maybe there was a kick option. We probably weren’t as clear in our comms and decision-making as we needed to be.
“There is nothing wrong with players challenging each other. We want that to be part of the group.
“Everyone is accountable, peer pressure is huge and we all need to take responsibility. That sort of criticism is not personal, it is about the individual getting better. We need people to be able to be critical.”
Both teams scored four tries in a barnstorming battle. Josh Adams, George North, Louis Rees-Zammit and Elliot Dee all crossed for Wales, who led 32-14 at one stage.
Waisea Nayacalevu, Lekima Tagitagivalu, Josua Tuisova and Mesake Doge grabbed scores for Fiji — who set up a nervy finale with two late tries.
Had Semi Radradra been able to hold a bounce pass then he would have scored in the corner and given Fiji the chance to secure victory via a last-gasp conversion. Wales clung on, however, for a pivotal opening win in Pool C.
“It is a pretty significant victory for us,” said Gatland. “Fiji probably went into the game as favourites, everyone expected them to win.
“We’ve always been a team that builds on confidence and gets better as tournaments go on. That’s exciting.”
Gatland’s side were also fortunate with the refereeing. Wales made a World Cup-record 248 tackles to claim the win. They received four warnings for repeated infringements but only lost one player, Corey Domachowski, to a yellow card.
Fiji, in contrast, had Tagitagivalu sin-binned in a sequence where only one penalty was conceded. Wales conceded a whopping 17 penalties and still prevailed, with their scramble defence proving resolute in the extreme despite the indiscipline. If Fiji’s coaches were fuming, they hid it well.
“We had opportunities and a chance to score at the end with the pass to win it,” said Fiji boss Simon Raiwalui.
“Wales had a couple of opportunities off our defensive errors and scored a couple of tries, and that was the difference. We’ve got a lot to work on.”
It was an emotional win for Biggar, with the clash falling on his late mother Liz’s birthday. “I hope she was looking down on him,” said Gatland.
Wales will not lack for motivation moving forward, both boosted by their rearguard action to secure victory over Fiji and also with a big battle against Australia ahead.
Beat the Aussies on September 24 and negotiate tricky clashes with Portugal and Georgia, and Wales would make the quarter-finals with something to spare.