Newcastle goalkeeper Shay Given kept the Irish in the match with a string of fine saves although his Montenegro counterpart Vukasin Poleksic needed to show sharp reactions to keep out a 56th-minute effort from Liverpool forward Robbie Keane.
"," said Trapattoni. "I told the players to be careful and in the first half they were a little bit stronger than us. But we were very well organised. We have a good defence and we played without little mistakes."
Given saved from Mirko Vucinic in the third and 74th minutes, but topped those efforts by somehow clawing away Stevan Jovetic's deflected shot in the 78th minute which was looking as if it might spin inside the post.
This draw following a 2-1 win over Georgia left the Republic with four points in a group eight also featuring world champions Italy, Bulgaria and Cyprus.