Robbie Keane, Aiden McGeady and Shane Long were on target as O'Neill and Roy Keane's opening game in charge ended well at the Aviva Stadium in Dublin on Friday night.
O'Neill spoke of the whole evening in glowing terms, although he sounded a note of caution looking ahead.
He told Sky Sports: "I am delighted with the team and with the performance.
"We have got sterner tests ahead - we know that - but it is nice to win and we played some good football too. It was an exhilarating night for us.
"We could have scored a few more but overall I am delighted with the team."
John O'Shea described the opening days of the tenure of managerial duo O'Neill and Roy Keane as "very positive".
It was an ideal start to the new era following the exit of Giovanni Trapatonni and defender O'Shea told Sky Sports: "It was a positive start.
"(It has all been) very positive: they are two natural winners and want the game played the right way.
"They know when we have to work hard and press teams when we have to and play when we have to."
Of the match, the Sunderland player added: "We needed a clean sheet and a couple of goals and thankfully we did that tonight.
"There were plenty of pleasing points and I look forward to a tough game in Poland."
James McCarthy echoed O'Shea's sentiments about the new managerial duo, saying: "He's come in and made us play out of the back today.
"We got a good result and hopefully that will continue.
"There is a real buzz around the place, we are all really enjoying it.2
Of Roy Keane, he added: "It is always brilliant to learn from such a footballing great."