Being two points behind leaders Manchester City, Arsenal need to beat Everton and hope West Ham can defeat City.
Arteta said: "Gabriel Jesus, we are in the last day of the season playing for the Premier League. The Premier League trophy hasn't been at the Emirates yet and it was built almost 20 years ago. That's a long, long time. We have to be very optimistic. The trophy is going to be there and it's possible we have to do our duties and then we wait and see what happens.
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"If I don't believe today then imagine how much I could believe in August. Then from August with 38 games against Man City, with what they've done in the last 12 or 13 years and what we've done in the last 20 years in the Premier League, we have zero chance then. We can't start like this.
"We have to believe that's for sure."