Arsenal manager Arsene Wenger admits his team are facing a fight to finish in the top four, but he still wants to catch Premier League leaders Chelsea.
Back-to-back league losses, including a 3-1 defeat at Chelsea last time out, have left Arsenal in fourth.
But they are just two points clear of sixth-placed Manchester United, while they trail Antonio Conte's side by 12.
Wenger said his team faced a battle late in the season to avoid finishing outside the top four for the first time since 1995-96.
"When you are a competitor you fight," he told UK newspapers.
"You fight as far as you can and we are in a double fight. We are in a fight to be in the top four, but we also have to fight because we want to catch Chelsea.
"We have to refuse to give up."
Wenger can get his team back on track when they host Hull City in the league on Saturday.
The Frenchman said his team needed to stay focused at what could be a decisive time of the season.
"It's as well an interesting week because it's a good test at an important moment of the season," Wenger said.
"And it's as well a good opportunity to show what we are made of and to deal with what matters to us - what is at stake and in front of us in the next game."