The Italian took time to praise goalkeeper Keiren Westwood, who kept a clean sheet in his first match as the new Irish No.1 following Shay Given's retirement from international football.
"Westwood showed that we can trust him to be a long-term replacement," Trapattoni told reporters. "I am also happy with the rest of the team although it was clear we still lack fitness.
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"We can take a lot of positives from this game because we were up against a well-drilled Serbian team who have some very good players in their ranks."
Trapattoni's counterpart for the night, Serbia coach Sinisa Mihajlovic, was also content with the result given the changes he has made to the national team due to the international retirements of key players Nemanja Vidic and Dejan Stankovic.
The former Fiorentina coach praised his team's defensive solidity and expected them to improve in attack during their upcoming World Cup qualifiers.
"We have made sweeping changes and it takes time to rebuild a team, but I remain optimistic about our chances of qualifying for the World Cup," Mihajlovic said.
"We were impressive at the back and I am confident that we will be able to add some bite to our attack before our opening qualifier against Scotland.
"We know our fans expect instant success but that's easier said than done and overall I am happy with our performance and the result."