Ireland's chances of qualifying for next summer's World Cup suffered a severe blow with a home defeat to the Swedes, leaving them three points off second place with three games to play.
Trapattoni admitted that Ireland's position in Group C looks precarious, conceding that anything other than victory over Austria on Tuesday will effectively end hopes of a trip to Brazil.
He told Sky Sports News: "I think we have done until now, a very, very great job, a great job. Not a good job, a great job.
"We have changed many players in the squad and in the team and before the game, we were level in the table with a great team like Sweden. Obviously, supporters when they lose in Italy, here, in England, they boo. It's normal. Obviously, we need to beat Austria.
"It's not easy because Austria also lost against Germany, but until the table says we are completely out, we must think [we can do it]. I must continue because there are another three games and in three games, anything can happen."