The Russia forward, who moved from Zenit St Petersburg to north London on the last day of the winter transfer window, has played three times for Arsenal and his performances have improved with each game.
"I watched the matches that were broadcast in Russia whenever possible," the 27-year-old told the Arsenal website.
"But to tell the truth it seemed less difficult on TV. Only now do I understand how dynamic and hard the football is here.
"Now I would like to score as soon as possible. Everybody expected me to score in my very first match but that never happens, especially with me. But nothing was easy and immediate for me.
"Arsenal is no exception. So I need patience and hard work now. The main task now is to get into the Champions League for next season."
Arshavin played in his favoured central playmaking role for 90 minutes at West Bromwich Albion on Tuesday night when Arsenal ended a run of four successive goalless draws in the league with a 3-1 win over the bottom side. He capped an impressive display with the free kick that led to Kolo Toure's first-half goal.
Arsenal remained in fifth place, three points behind Aston Villa whose game in hand was due to be played against Manchester City later on Wednesday.
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