The England international was sent off for two bookable offences against Manchester United, in only his second appearance since missing 14 months of football through injury.
The 20-year-old accepts responsibility for his suspension, and is now focusing on preparing himself for the clash against Spurs a week on Saturday.
"I am gutted to miss Saturday [against Fulham] after being out for so long, it’s a disappointment to miss any game," Wilshere told the Gunners' official website.
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"When you see it [the challenge that earned him a second yellow card] in slow motion, it looks like a bad tackle but honestly I didn’t mean to go for him [Patrice Evra]. I just went for the ball.
"When he sent me off I was shocked but when I saw it after, I can see why he sent me off."
Defeat against United leaves the Gunners nine points adrift of the league leaders in seventh place, but Wilshere insists that his side can still compete for the title.
"The target is the same - we need to challenge for the Premier League," he said. "OK, we are a bit far behind now but we really need to step it up.
"We have dropped a few points and we can't afford to be dropping points now. We know we need the top four but if we can get anything more, then we push on every season. That’s the aim.
"The aim at the beginning of every season is to challenge for the Premier League and win a trophy. It's no different this year."