The sixth-placed Londoners, 15 points behind leaders Chelsea, have received criticism from fans this season after a string of lacklustre performances.
But with three games in seven days, starting with the visit of Queens Park Rangers to the Emirates Stadium on Friday before away trips to West Ham United and Southampton, Wenger has urged his side to prove their doubters wrong.
"We have a good opportunity over Christmas to show that we are much better than people think we are," the Frenchman told a news conference.
"There are three games in a very short period of time and we can make points. Our opponents will think that as well, but let's just put the performances in and capitalise on it.
"The consistency in that period is what will matter."
Arsenal will have to deal with in form QPR striker Charlie Austin, who scored a hat-trick against West Bromwich Albion last weekend, and Wenger praised the 25-year-old for the way he has risen through the English lower leagues.
"It's good to see that an English striker who had played in lower divisions has managed to come up," said Wenger. "That shows mental strength and tenacity -- and that is important at the top level.
"It could bring on the idea that there could be other players down there who are good enough to come up to the Premier League but don't get a chance."
Arsenal's progress this season has been hindered by a number of injuries, but Wenger expects Mesut Ozil and Mikel Arteta to return to action in January, while Theo Walcott, Aaron Ramsey and Laurent Koscielny are due back in the near future.
With the Gunners chasing a top four finish and still competing in the Champions League and FA Cup, Wenger is hoping 2015 will be a profitable year.
"I believe that with the injuries coming back we will have a much stronger squad than we have had for the past two months," he said.
"I believe 2015 can be very exciting if we manage to get our injured players back and have a good run."
(editing by Justin Palmer)
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