A 1-1 draw at the Vasil Levski Stadium in Sofia kept the Irish five points clear of their hosts in Group 8 with world champions Italy only a point better off.
However, the vastly experienced Italian knows there is still a long way to go before he or his players can start to think about South Africa.
He said: "Today we have a little advantage, but only a little advantage. I do not talk about percentages. I know that wood is wood and the ground is the ground.
"I always thought that this was going to be a more difficult game for us than Italy away because Bulgaria are a very dangerous team. They showed that tonight when we conceded the goal so soon after scoring and I was a bit afraid we would lose the game.
"But I am happy now with the good result. We have a long way to go yet before we can talk about South Africa. I have always said that it will be a long qualifying campaign, but I am happy with this result."
Ireland got off to a flying start when central defender Richard Dunne, who only played in the game after having a pain-killing injection in his knee, headed them into a 24th-minute lead.
However, the Bulgarians were back on level terms within five minutes when midfielder Dimitar Tekiyski took full advantage of a slip by Kevin Kilbane to level.
From then on, the visitors were forced to weather a storm, but with keeper Shay Given having few saves of any note to make, they toughed it out to extend their unbeaten run in competitive games under Trapattoni to seven.
The Republic were indebted to the immense Dunne for his bravery in defence, and there were also notable mentions for Sean St Ledger and Caleb Folan, who looked far from out of place in their first competitive starts.
Trapattoni said: "I am happy that now we have a bigger squad. When I took over, I felt our squad was little, but now it is big with these new and young players.
"St Ledger showed us tonight that he is a clever player, also Folan and [substitute Leon] Best. And I know what Richard Dunne does for Ireland every game, as he did again tonight."
Ireland resume their campaign in Cyprus in September before home games against Italy and Montenegro bring the campaign to a conclusion.
Skipper Robbie Keane, who was substituted for the first time in four years playing for his country after he finally succumbed to the foot injury which had hampered him all week, is delighted with the position his side has got itself into.
He said: "There are still a few games to go, but it was important we came here today and didn't lose, so that was a big plus for us. If we had lost today, it would have put them [Bulgaria] right back in it with a chance.
"But now it puts them slightly behind us, and Cyprus drew as well, so that's a decent result for us. It keeps a few teams away from us and at the moment, it's just between ourselves and Italy."
Bulgaria, however, now face an uphill struggle even to claim the runners-up spot. Manager Stanimir Stoilov said: "We have to rely on our rivals to make mistakes now if we are going to make it to the World Cup finals. I do believe in miracles in football and they have happened for Bulgaria before."