Scotland were humiliated by the Pacific islanders and Robinson's position will come under scrutiny for the second time this year. The coach led the side to their first Six Nations whitewash since 2004 – ending a season in which they had also failed to make the group stage of the World Cup – and he has now overseen a clean sweep of autumn Test defeats as well.
It is the first time Scotland have gone a whole year without a Test win on home soil since 1998.
"That performance was totally unacceptable," said Robinson, struggling to control his rage. "I am very angry about what I've seen and I would like to apologise to the supporters.
"There will be consequences because of this performance. I won't go through what those will be yet, but from my side that was totally unacceptable."
Robinson was asked if he would consider his own position. It is normal protocol for Scotland coaches to debrief their SRU employers after each international period, and Robinson will meet chief executive Mark Dodson to deliver his assessment of the losses to New Zealand, South Africa and Tonga they have sustained over the past three weeks.
"It reflects on me," said Robinson grimly. "After the South Africa and New Zealand games I thought there was progress. Today there was not. It was hugely frustrating to watch because we knew what was coming. This is rugby at the highest level.
"I will meet with Mark, but that's between Mark and myself. I have a contract to 2015. After the performance we have seen today there have to be consequences for what happened. I will be at the forefront of those discussions."
Kelly Brown, who has yet to taste victory as Scotland captain, backed up the coach's comments: "We have shown that when we nail it and play as we can then we can put any side under pressure," he said. "We're not doing that for 80 minutes and not doing it week after week. That's something we need to look at. As Andy said, it's not acceptable to let our standards slip to where they were out there today."
However, Brown defended his decision not to kick relatively straightforward penalty chances in the first half, claiming he felt Scotland had the Tongans under pressure and that they had a good chance of getting a try instead.
"It is really about taking our chances," said Brown. "That's something I will be looking at. The coaches aren't out there on the pitch, it's up to the players. We need to look inside ourselves."
Understandably, the Tongans took a different view of things.
"I am very proud," said Mana Otai. "The performance could have been better, and we all know that, but what can you say? They did very well. But the boys made a bit of history today."
Tonga captain Nila Latu was just as delighted. "We came into this game wanting to win," said Latu. "It didn't really matter how we won. It was important for our country, for our nation. The boys showed a lot of guts.
"We went into the changing room positive and wanting to come out and put Scotland under pressure in the second half. We were hugely up for it today. It was a great effort because we had so much to lose."