Arsène Wenger believes Arsenal still have a “good chance” of a top-four finish, after watching Alexis Sánchez inspire a nervy 2-0 home win over a Sunderland team that fought throughout, despite the fact they were already relegated.

The Arsenal manager knows that his club will need a favour from either Middlesbrough, who visit Liverpool on Sunday– the final day of the Premier League season – or Watford, who host Manchester City.

Arsenal’s top-four hopes intact as Alexis Sánchez ends Sunderland’s resistance Read more

But, as he demanded that those teams put in the same effort as Sunderland did here, he retained hope. Arsenal return to the Emirates Stadium on Sunday to face Everton. They sit one point behind fourth-placed Liverpool and three behind City, who are third.

“I don’t think about the percentages,” Wenger said. “I just think: ‘Let’s make sure we win against Everton.’ Even if you have only a 1% chance, you would have to play totally at 100% but I think we have a good chance. If we won, it would be the first time you make 75 points and you are not in the top four.

“I answer for 20 years the question: ‘Is the top four nothing special?’ I don’t know why, suddenly, it could become such a big problem [not to finish in the top four]. I am quite surprised. I want to make sure, absolutely, that we are in there but let’s get to 75 points and see what happens. You want all the teams to fight like Sunderland did tonight and, after, you have to accept the result.”

Sánchez scored both of the goals towards the end of the game, having shaken off the thigh problem that had threatened his participation. “I made the decision to start him at 4pm,” Wenger said. “I felt he had something still left. Once he is on the pitch and has the ball, he becomes the devil and forgets his pain.”

Wenger claimed not to have noticed the massive number of empty seats inside the stadium or to care about them. It had felt like the latest protest against him and his desire to continue into next season.

Play Video 1:03 Wenger: Arsenal have 'good chance' of top-four finish – video

“It’s a Tuesday night against Sunderland, who everyone expects us to beat,” Wenger said. “When you play football, you do not count how many people are sitting in the stand. We do our job and we have done that tonight. Will it be full against Everton? We are sold out.”

The Sunderland manager, David Moyes, took issue with Wenger’s pre-match comments about how teams with nothing left to play for were sometimes “on holiday.” Moyes said: “That’s an insult to footballers. When you are brought up in this country, you are brought up to show that every game matters.”