Trapattoni's side secured second place in Group B with a 2-1 win over Armenia at the Aviva Stadium on Tuesday and now they await their fate in Thursday's draw in Krakow.
The Irish are one of eight teams, the others being Turkey, Estonia, Bosnia-Herzegovina, Croatia, Montenegro, Portugal and the Czech Republic, still hoping to secure a place at next year's finals in Poland and the Ukraine.
The first legs will take place on either 11 or 12 November, with the second legs on 15 November.
While the play-offs have often been unkind to Ireland in the past, Trapattoni believes his team are capable of holding their own against any of their potential rivals.
Ireland's task could be easier this time as they seem likely to be seeded along with Portugal, Croatia and the Czechs, but Trapattoni is happy to accept whatever fate sends their way.
"All the second-placed teams are very important. We must accept whichever team," he said. "The first and second teams in the table are always great teams. But I think it would be better to play the first game away and the second at home.
"We have only done 50 per cent of the job because there is now the play-off. All opponents are not the same. Maybe the next won't be as good as Armenia."
Ireland reached the play-offs in controversial fashion with a hard-fought victory over Armenia, who caused them problems throughout despite having goalkeeper Roman Berezovsky harshly sent off after just 26 minutes. Berezovsky was dismissed when he blocked Simon Cox's shot outside his penalty area.
While that was cruel on Armenia, the visitors shot themselves in the foot when defender Valeri Aleksanyan turned Damien Duff's driven cross into his own net in the 43rd minute. Ireland looked to be cruising when Richard Dunne bundled home after substitute keeper Arsen Petrosyan had failed to cut out Aiden McGeady's 60th-minute cross. But Henrik Mkhitaryan's strike two minutes later dragged the 10 men back into it and sparked a fightback which came up just short despite Kevin Doyle's 81st-minute dismissal for a second bookable offence.
Test of character
Trapattoni admitted his side had been second-best before the break, but was delighted with the character they showed to pull through. "Armenia in the first half played very, very, very well and it was very difficult to control the game," he said. "They had more possession, yes, they played better than us, yes, in the first half, but I don't remember any particularly difficult situations for us."
Trapattoni's only disappointment was the red card which will prevent Doyle from playing in the first leg of next month's play-off. "I want to see it again. I immediately asked the linesman and he said he had used his elbow. But that's not Kevin Doyle," Trapattoni said.
Armenia coach Vardan Minasyan added: "Congratulations to the Irish team, I wish you luck in the play-off. "You are a very good team, but I am very proud of my team. We have done a very good job and we can be proud."