Ozil made an impressive start for the Gunners when he joined from Real Madrid last September, but the Germany international has come in for criticism in recent weeks.
"I'm going through a test of character here," he told Germany's Bild am Sonntag newspaper.
"I have so much self-confidence as a player that I am ready now to take the next step.
"But first you have to get used to the intensity of the Premier League."
Meanwhile, Ozil says he cannot wait to face Bayern Munich in the Champions League on Wednesday night.
The Gunners went closer than anybody to knocking Bayern out of Europe last season, losing on away goals after a 2-0 win at the Allianz Arena failed to overturn a 3-1 loss at home in the first leg.
Goals from Toni Kroos and Thomas Muller put the visitors in the ascendancy at the Emirates and although Lukas Podolski pulled one back, Mario Mandzukic increased Bayern's advantage.
Olivier Giroud and Laurent Koscielny scored in Munich to set up a nail-biting finish to the last-16 tie, but it was the Germans who progressed.
Ozil believes Arsenal face an even taller order to get through to the quarter-finals this time round, as he feels the cup holders are even stronger under Pep Guardiola than they were last season.
"I have huge respect for Bayern," added the 25-year-old.
"They are even better than they were last year, but we're not going to hide.
"Anything is possible over two legs. I'm the kind of player who loves games like these."
Aside from the Gunners' quest for the Champions League and Premier League title - they are second, a point behind Chelsea - Ozil's personal goal is to win June's World Cup in Brazil.
"Anyone who has ever played at Real will always want to win titles," said Ozil.
"When you've prepared so hard and intensively for a World Cup as we have, then your goal isn't to finish second or third."