The Gunners lost 3-2 at Old Trafford and 2-1 at home to Swansea to slip six points behind leaders Leicester.
"Sometimes we lack the mentality that we are already winning 1-0 when we go out on to the pitch," Sanchez told Directv Sports before the United match.
"We lack this hunger to believe that we can be champions."
Sanchez added: "If we go out onto to the pitch with hunger to become champions, to win the Premier League or the Champions League we can achieve it.
"I remember a game against Manchester United last year. The lads looked hungry for silverware as we took to the pitch.
"We crushed them in the first 20 minutes and went 3-0 up. We were hungry and brimming with confidence that day."
Arsenal have only three wins from 11 games in all competitions and are third in the league.
Speaking after Wednesday's loss to Swansea, Gunners manager Arsene Wenger also said his side's loss of form "looks a bit" like a confidence issue.
"I am worrying about our results," he said. "We don't dream. We have to be realistic and come back to what we do well... the basics.
"The players are very down but we have to respond. We have to focus on our job and remind ourselves that we have some quality as well."

Mr Trump called it a "very precarious" issue for the party and said that Mr Cruz's nomination could be challenged in court.
Mr Cruz was born in Calgary to an American mother and a Cuban father.
Most legal experts believe Mr Cruz meets the requirements to be president.
The Cruz campaign responded by saying Mr Trump had "jumped the shark" - a pop culture reference to when a TV show or fad has overreached and fallen into decline.
The Texas senator is performing well in polling in the early voting state of Iowa. While Mr Trump leads most polls, several surveys show Mr Cruz is the top choice of likely Republican voters.
Much of Mr Trump's support comes from independents, disillusioned Democrats and people who have never voted before.
Some analysts are predicting that Mr Cruz will win because of how the voting process is structured in Iowa.
The caucus format requires more time and dedication from voters than a typical US primary election.
Before Mr Trump became a presidential candidate, the New York businessman had repeatedly questioned President Barack Obama's citizenship.
Mr Obama was born in Hawaii to an American mother and a Kenyan father.
Authorities in Hawaii and Mr Obama both provided detailed birth records after some conservatives such as Mr Trump questioned where he was born.
Mr Obama's allies have said the "birther" movement was a racist effort to discredit the county's first black president.
Alexis Sanchez said Arsenal lacked the self-belief to win the Premier League even before their back-to-back defeats by Manchester United and Swansea.
[NEXT_CONCEPT]
Republican presidential front-runner Donald Trump has questioned whether rival candidate Ted Cruz is eligible to become his party's nominee because he was born in Canada.