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Manuel Marini appeared to have twisted the knife into Staunton with an equaliser six minutes from the end of normal time, with that goal cancelling out Kevin Kilbane's 49th-minute opener at the Serravalle Stadium.
But with San Marino standing on the brink of clinching their first point in their European Championship history following 37 consecutive defeats, Manchester City midfielder Stephen Ireland tapped home from eight yards.
That did not stop irate fans from booing the team, criticising Staunton, as well as calling for the head of Football Association of Ireland chief executive John Delaney.
When asked for his message to the disgruntled supporters, a defiant Staunton replied: 'We will keep going. Obviously, we are angry ourselves but we are rebuilding and trying to look forward.
'We don't like coming here and just scraping through, but you have to see the other side of this in that we have enough character to win in the end and that's the main thing.'
A direct question was put to Staunton as to whether he would have considered his position if San Marino had conjured up a point, but again he stood firm as he replied: 'No, not at all.'
But coming just four months after the 5-2 humiliation to Cyprus in Nicosia, it remains to be seen as to just how many more poor results Staunton can withstand.
This match bore the hallmarks of another infamous night in Ireland's football history when they were held to a goalless draw by Liechtenstein in a 1995 European Championship qualifier.
Referring to that, Staunton said: 'We were looking at Liechtenstein all over again. Following this, my overriding emotion is one of relief, but we showed tremendous heart, spirit and fight. We created three or four chances after they scored, and eventually we took one to win the game.
'After going 1-0 up in the second half I thought we would go on to win comfortably. We didn't, but what more can I say, we've got three points and we keep moving on.
'Clearly, the players are disappointed with the performance, but again you cannot question their attitude. We controlled the game from start to finish apart from the one mix-up for their goal, and thankfully Stephen Ireland got us out of a hole.'
On the San Marino goal, Stanton said: 'It was very poor. There was a complete lack of concentration. But every team you play against, no matter who they are, will always get a chance.'