The Chilean played 74 minutes as Arsenal lost 1-0 to Monaco in the Emirates Cup on Sunday, having come off the bench during a 5-1 demolition of Benfica a day earlier.
Alexis, who joined from Barcelona last month, is keen to settle as soon as possible and believes his game time over the weekend will prove hugely beneficial.
"I have to go step by step, I have only trained twice with the team," he told the club's official website. "Today I played 70 minutes, I believe I needed it, and I just have to keep on working hard and training.
"I like this style of football. What is important for me now is to try to play games, to score as many goals as possible and to win titles.
"What is important now is to play and get fit. I need to get 100 per cent."
The 25-year-old also thanked Arsenal's fans for his warm reception.
"Of course I loved it, I am extremely thankful to all of them," Alexis added.
"I am extremely happy and I hope I can make them very happy as well."
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