The Danes were closing on an important victory on Friday night when Aquilani struck at the death to secure the Azzurri a 2-2 draw in Copenhagen.
"It was certainly a shock for Denmark," Aquilani said to Italian broadcaster Rai. "But these things happen in football. It was a fortunate goal."
The Italians trailed 2-1 with 12 minutes remaining before the Fiorentina midfielder met Dani Osvaldo's cross and notched his team's second goal.
"It's my first Italy goal played away from home," Aquilani said. "I thought I might have been offside, but I wasn't.
"When you play in these stadiums it is always complicated, as Denmark were giving their all to earn qualification.
"We were fortunate in some occasions, conceded when we shouldn't have done, so in the end the draw was the right result."
Italy coach Cesare Prandelli had expected his team to play better.
"We know there are moments where you mustn't drop the concentration," Prandelli said. "We dropped back by 10 metres before the break and allowed Denmark to put those crosses in and equalise.
"After a very good first half, we suffered especially after the restart.
"For 20 minutes, we only thought about defending.
"This team, however, is used to playing and if you lose that peculiar quality then you become vulnerable."
Italy, who have collected six wins from nine qualifying games and went into Friday night's match with their spot at next summer's World Cup finals already secured, end the campaign against Armenia in Naples on Tuesday.
The Azzurri will be hoping to welcome back AC Milan striker Mario Balotelli, who missed the Copenhagen encounter with a fever.
"Mario had a bit of a fever and we hope to recover him for Tuesday's game," Prandelli said. "In Naples, we will find another team ready to battle.
"Bulgaria, Denmark and Armenia all have the possibility to finish second of the group but we want to end the group unbeaten."