The scoreless draw meant Ireland slip off the top of Group B, with Russia's 1-0 victory over FYR Macedonia in Moscow earlier in the night ensuring Dick Advocaat's men are at the summit, ahead of Ireland's visit on Tuesday.
Ireland must win in Moscow to keep the fate of the group in their own hands, and despite the disappointment clouding the Aviva stadium, the Italian coach was adamant that victory was not out of the question.
"We must think that it is possible to win in Moscow," he said. "It's not easy, but with this mentality, I think we must be able to think ahead.
"This is the first game we haven't scored [since I arrived], until now we have always scored goals. We didn't concede to our opponent and we deserved more, we have the possibility to deserve more."
Ireland did indeed have the chances to get more from the game, but they were few and far between and when they arrived, the players looked ill-equipped to take them.
Damien Duff's first-half snapshot brought a good save from Jan Mucha, but there were few clear chances until later in the game, after Slovakia had seriously threatened to breach the Irish defence.
Duff provided an inch-perfect cross with 16 minutes remaining that Robbie Keane somehow put over the bar from six yards out, while substitute Simon Cox also pushed an effort wide as the clock ticked down.
"My opinion is that in the first half Slovakia were a little physically superior and had more possession," said Trapattoni. "But in the second half we had two or three chances with Dunne, Keane and then Cox.
"I am disappointed that with three big opportunities that we did not score one goal. But we did not lose and that is important. We had balance on the pitch."
They have now taken four points from their trips to Dublin and Moscow, and Weiss is hopeful Ireland can take points from their trip to Russia too.
"It was a great match, it was open so we could have won and we could have lost," he said. "In this match everything was possible.
"In the group everything is open, we have a good chance for the future. I hope for the same result for Ireland in Moscow. We are in the same position as Ireland now, we have games against Armenia and Russia at home and then Macedonia away."