The Manchester City playmaker stated that Les Bleus did not go for a win against the Three Lions, but a change in approach was enough to see off Oleg Blokhin's men
Goals from Jeremy Menez and Yohan Cabaye sent Laurent Blanc's men top of the group as Les Bleus triumphed 2-0 against the Yellow-Blues.
But the Manchester City playmaker revealed that Les Bleus were motivated to win, and did not play in the conservative manner that was on display against Roy Hodgson's men.
"We really had a different mindset to the first game," Nasri told reporters after the victory.
"Ukraine were prevented from playing. There could have been 200,000 Ukrainian fans in the stadium, we wanted to win this game so much that it would have happened anyway.
"We had the heart to win this game, the opposite of what we did against England."
The winners of Group D will avoid the probable Group C victors Spain, but the ex-Arsenal midfielder does not feel that this is a priority.
"We want to qualify. Whether we play Spain or not in the quarter-finals, it will be hard.
"If you want to excel in this tournament you will have to play and beat the Spaniards and other big teams," he concluded.
France's third and final group game against already-eliminated Sweden kicks off at 20:45CET on Tuesday.