The Spanish international joined the club from Malaga on transfer deadline day, and has impressed many fans with his start to his Gunners career.
The £8.7m signing is determined to bring success to his new employers.
"I'm asked to defend well and not so much to score goals," Monreal told The Sun. "When I go forward and assist others, it is as if I have scored, so that is a great satisfaction for me.
"I am a committed person and so give 100% in every game. That is the best attribute a footballer can have: that every Saturday you give everything you have for your team.
"I cannot complain about my career but I would like to win a trophy - and I hope I can do this with Arsenal."
Arsenal host Blackburn Rovers in the FA Cup on Saturday.