Kazakhstan took a spectacular 13th-minute lead through Dmitriy Shomko's 25-yard strike at the Aviva Stadium in Dublin on Tuesday night, but the Republic hit back in style, with Robbie Keane levelling from the penalty spot just four minutes later and O'Shea putting the hosts ahead just before the half-hour mark.
A late own goal from Dmitry Shomko sealed the win for the Republic as they finished disappointing World Cup qualifying campaign on a high note under interim boss Noel King.
Asked if it was a good way to end, O'Shea told Sky Sports: "We would have liked a clean sheet but it was a hell of a strike from the lad to put us a goal behind, but I thought the reaction straight away from the lads was fantastic.
"Noel said to us beforehand that whatever happens, if they score a great goal or whatever, keep your heads up and play properly. We got the rewards from it and we could have scored even more."
Regarding his goal, which was first at international level in 10 years, O'Shea added: "The goal gave us a bit of relief because we started quite well but their goal upset us a bit, but like I said the reaction was fantastic and we gave the crowd a little something to cheer."
Looking to the future and what sort of manager he would like to take over on a permanent basis, the Sunderland defender said: "We want someone positive, we want someone who knows us all.
"Who ever gets it, gets it, and they know they'll have a good group of lads to work from and a team that's hungry to qualify for the next European Championships."
It was not all good news for Ireland though, as midfielder Darron Gibson was carried from the field on a stretcher with suspected knee ligament damage.
James McCarthy, who is a club-mate of Gibson's at Everton, hopes the injury is not as bad as feared and admits any long-term absence would be a huge setback for the Toffees and Ireland.
He said: "Hopefully he's OK, we wish him a speedy recovery. If he's out for a long time, hopefully he's not, it would be a massive blow for club and country."