The Frenchman has enjoyed a promising maiden campaign for the Gunners and commended the side for wrapping up a top-four finish, but maintained it must progress in Europe
Arsene Wenger's side will be required to qualify for the group stage in August after sealing fourth-place on the final day of the season ahead of rivals Tottenham.
Although the Gunners will compete in Europe's elite competition for the 17th consecutive campaign, the north Londoners have fallen below expectations in recent seasons, suffering elimination at the last 16 stage for the third year in a row after losing on away goals to Bayern Munich.
Giroud was keen to praise the efforts of his team-mates, before switching his attention to next season's Champions League - a tournament he feels the club must make better progress in.
"On the bench [against Newcastle] it was really nervous," Giroud told the club's official website. "It's always worse when you don't play. It was really difficult but in the second half Laurent [Koscielny], my French friend [scored]. I'm so happy that he scored.
"The goal relieved us and we could dominate the game after. We became more confident. We had our destiny in our hands. It was very difficult but the finish was amazing.
"It's 16 years in a row we've succeeded to qualify for the Champions League. We knew it was really important. For me it will be the second season in the Champions League.
"When you play in the Champions League, you always improve yourself and it's better for competition.
"We are competitors and want to play in the top games. I really enjoy playing against big clubs like Bayern Munich. I would like to go further next year."
After making the switch to Emirates Stadium from Montpellier last summer, Giroud netted 17 times in 47 games (all competitions) in his debut season at Arsenal.