And he also insists Arsenal can be proud of their season given the injuries suffered by frontline players.
He said: "Obviously we can't win it but we still want to do as well as possible and get second place, which is really important. We just want to win games, which we know we can.
"This season, we've had a difficult time with injuries and I think we've done well with that. You see other teams that have had big injuries and they're not sitting very well in the league.
"So yes, we've had some big injuries and I believe that it's a credit to all the players that have come in and done so well."
Plenty to look forward to
White also insists he's now fully recovered from long-term injury this season.
He continued: "I've never really been injured before. I didn't really know how to deal with it as well as I probably could have.
"It's just so long, not doing what you love and not being able to help the team was tough. I'm back now, feeling good and I think it's about getting ready for next season.
"I'm having a baby this summer so I'm going to be in England, training every day and getting back to my best. It's something so exciting and probably the most valuable thing you can have happen."