Manchester City striker Stephen Elliott pulled a goal back before Blackburn defender John Fitzgerald struck a last-minute equaliser to give the Irish a deserved draw.
"This group have come through together, they have been to the World Cup and done well, and they have an inner confidence that they are difficult to beat and they proved it again today. It is a great quality to have, although you need technical ability too," said Givens.
"I felt we created three times as many chances as them and we were the away team so I am happy. We missed a few chances and got caught but that's part of the learning curve for the boys.
"At half-time I told them to change nothing and just keep going. Unfortunately, we let another goal in but, even at 2-0, I never felt we would lose the match. I felt we'd get it back because we were playing well.
"I thought it was a good game and I was happy with my team's performance because we created a lot of chances and were happy in the end not to lose the game.
"We have had a good series of games ... and we were very keen to continue the run. To come to Poland, who are a good team, and not lose ... I am quite happy tonight."
Ireland's unbeaten run looked in danger after twin brothers Pawel and Piotr Brozek scored a goal each but Elliott pulled one back in the 63rd minute, before Fitzgerald became the last-gasp hero.
The Poles had been hoping for revenge after crashing 5-1 to the Irish last August.
Ireland fell behind when Poland captain Antoni Lukasiewicz's long ball over the top into the left channel was taken down nicely by Pawel Brozek, who held off debutant Paddy McCarthy before slotting the ball through Wayne Henderson's legs at the near post.
Ireland came close to equalising after 32 minutes when the Polish goalkeeper dropped a deep cross. Sunderland's Sean Thornton pounced, but his shot was cleared off the line by Lukasiewicz.
Poland scored again after 53 minutes, and this time it was Piotr Brozek who was celebrating. Piotr played a one-two with Pawel Brozek and slotted the ball past Henderson.
After 66 minutes, Henderson prevented Ireland from falling further behind with a fine block to deny substitute Pawel Mielniczek and that proved a turning point as the visitors went straight up field and pulled a goal back.
It was Elliott scorer of a hat-trick in win in Gdansk last time who coolly slipped past the goalkeeper and slotted the ball home from the right edge of the box.
Ireland never gave up and eventually grabbed their equaliser.
Thornton floated in a deep free-kick to the left-hand post. Fitzgerald headed the ball down, and Elliott's shot was blocked by the goalkeeper. But Blackburn's Fitzgerald rifled home the rebound.
: Cierzniak, Wojtkowiak, Kucharski, Lukasiewicz, Dudka, Strak, Szalachowski, Zganiacz, Pawel Brozek, Piotr Brozek, Gregorek.
: Henderson, Kelly, Capper, Fitzgerald, McCarthy, Whelan, Flood, Potter, Elliott, Doyle, Thornton.
: Z Bakaluk (Poland).