Arsenal, who are back in the Champions League for the first time since the 2016-17 campaign, face PSV Eindhoven, Europa League winners Sevilla and RC Lens in Group B.
"Every time I watched (the Champions League) and we weren't there, I felt it. This club has to be in the Champions League," Arteta told reporters ahead of Wednesday's game against PSV at the Emirates.
"It was a process but we are here and now we have to make the most out of it. It is always a learning process. I think we did and we have improved in a team, we have improved the squad and we deserve to be here...
"We are proud and excited. It has been a long time for the club since we have been in the competition, and for me it is the first time as a manager, so I am really looking forward to it."
The English club crossed paths with PSV in last year's Europa League, with both sides winning their respective home fixtures in the group stage.
"We have to treat it like any other game. We are used to playing tough opposition every week in the Premier League. It will not be any different tomorrow," Arteta said.
"Tomorrow we are going to play against a really good team. They are used to winning and it will be a really tough test, I am sure about that."
Arsenal will be without forward Gabriel Martinelli, who was forced off with a muscle injury in their 1-0 Premier League win at Everton on Sunday.
"He felt something in his hamstring. We need to do some further tests," Arteta said, adding that there was a "possibility" that the Brazilian could be fit in time to face rivals Tottenham Hotspur in the league on Sunday.
