Arsenal manager Arsene Wenger says his team deserved the win against Southampton on Wednesday night.
The Gunners struggled against Ronald Koeman's side in the first half but improved in the second half as they took all three points from the Emirates.
"I think we deserved it [to win], yes, because we have very few chances away and we had more chances than Southampton," Wenger said.
"We kept a clean sheet as well.
"It was difficult for us to keep going from the start of the game because we've given a lot against Dortmund and on Saturday - today was the third game in seven days.
"You could see that we had to dig deep. We played against a good team who are very well organised and play very quick on the counter-attack. For us it was important not to be exposed on the counter-attack and to keep a clean sheet.
"We had to be patient and wait for our chances and you could see in the last 20 minutes that they started to suffer a little bit physically and that we created openings."
Alexis Sanchez was again the hero for the Gunners, much to the delighted of the Frenchman.
"He [Sanchez] was one of the players who had to dig in today but he still has such a desire to fight, which is why he always finds something special to get the goal," Wenger said.
"It's difficult to find examples of people who have settled so quickly. My memory is not perfect but quicker, you cannot.
"We are in December and he arrived in July - when you look at the number of goals and the impact he has on the team, it's fabulous."
The manager was also full of praise for centre back Laurent Koscielny, who produced a superb block to deny Graziano Pelle in the second half.
"Laurent Koscielny was absolutely outstanding today," said Wenger.
"He contributes to stabilise our defence. We missed him for nearly two months and it's important."
