Sanchez, who is the club's leading scorer with 23 goals and 10 assists this season, said that his team could perform better.
"Sometimes when I look at the team we have and the players here... when it comes to winning the Premier League we often lose or draw against teams at home when we are superior," Sanchez told British media.
"Sometimes the frustration more than anything is about the fact we could be challenging for the Premier League title."
Sanchez also said that the players' mentality is the reason for their recent three-game winning streak in the league.
"I've always said we have great players here, it's just about having the mentality of being a great player and going out on to the pitch already thinking about winning," he said.
"That's what we've done in the last three games. We had the mentality to win at all costs and we won and we won well."
Arsenal trail fourth-placed Liverpool by a point with one game left in the season and risk missing a Champions League spot for the first time during manager Arsene Wenger's 20-year reign at the club.
Arsenal can, however, win the FA Cup for the third time in four years when they face Chelsea in the final on May 27 but Sanchez remains uncertain if that would make the season a success.
"I don't know whether it would be successful or not, but I think it would be positive to beat Chelsea in the FA Cup final," he added. "I think the players have the desire and mentality."
Arsenal must beat Everton on Sunday and can finish fourth if relegated Middlesbrough draw with or win against Liverpool the same day.
(Reporting by Aditi Prakash in Bengaluru; Editing by Amlan Chakraborty)
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