The Southampton striker handed his side the lead in the first half before setting up Alberto Aquilani for a dramatic late equaliser in the 2-2 draw in Copenhagen.
And the 27-year-old is determined to remain in Cesare Prandelli's plans after a year of international uncertainty, during which he was left out of the squad for Euro 2012 before being kicked out of the party for this summer's Confederations Cup after a spat with interim Roma boss Aurelio Andreazzoli.
At the end the result was fair, he told Rai Sport of the encounter with Denmark. When I'm called up I think about giving my best, then the coach will decide.
I like to play, but I'm just glad to be part of this group. Prandelli always has nice words for me and I try to pay him back on the pitch.
Osvaldo joined Southampton from Roma this summer for a fee in the region of €15 million, but he insists he is delighted to see his former side performing well under new boss Rudi Garcia following their unbeaten start to the Serie A season.
I'm delighted Roma are top of the table, he added. I have many friends there and I miss the dressing room and my friendships there. I hope they carry on like this.
Regardless of everything that's been said, I was fine with everyone and we loved each other. Now I am calm and peaceful in England and I hope the results keep coming.
Alberto Aquilani bundled home a fortuitous Azzurri equaliser in stoppage-time after Nicklas Bendtner struck twice for the home side on Friday, and the Fiorentina midfielder acknowledged it was a good result for his side given the determination displayed by Morten Olsen's outfit.
Mine was a lucky goal, Osvaldo did well to aim at my knee, Aquilani said.
It was a difficult test. Denmark played the game of their life and we saw that on the pitch. We started well, but at the end of the first half we eased off.
