The Gunners triumphed in their top-of-the-table Premier League clash against Liverpool last Saturday and then ended Borussia Dortmund's eight-game home winning streak in the Champions League three days later by recording a 1-0 success in Germany.
They face another stern test of their title credentials today when they visit Old Trafford to play current holders Manchester United, but Ozil has insisted that Arsenal do not fear any opposition.
"The message after Wednesday's win is that now Arsenal can beat any team in Europe," he told The Sun. "Maybe in the past they have struggled against some bigger clubs. But, as of this week, we have shown we can beat any team. And now we realise the big players all around the world have a huge respect for us.
"I knew before I signed that Arsenal were a high-quality club so I never considered it a gamble to join them. I also knew they had one of the best coaches in the world, who always puts his team first and allows his players to develop and to grow.
"And after talking with Arsene Wenger I was very quickly convinced that moving to London was right for me. The aim is to achieve success this season - and we want to do that by having fun as a team."
Ozil has made 12 Gunners appearance since arriving for £42m from Real Madrid on transfer deadline day, scoring three goals and assisting five more in the process.