Wenger said: "If you ask me whether I want to win the Champions League, I'd say 'Yes, of course'.
"But at the end of my career I don't think I will ask every day 'Do I commit suicide because I haven't won the Champions League?' Hopefully, it will never come to that. I hope I'll have won it before I retire. Come back and ask me that question again just before I die."
He added: "I'm sure I'm not the only one who does that. I think Thierry Henry is probably replaying those two chances he had as well. So let's make it happen this year. We're already in the quarter-finals, so let's go for it."
Wenger's No1 target is the Premier League despite surrendering a six-point lead to bitter rivals Manchester United in recent weeks.
He insisted: "You think I have been fighting in the league since the first day of the season to finish second? Don't count on us giving up now after we have given absolutely everything. We believe we can still win the title and it is not impossible.
"Manchester United still have six games to go and four of them are away. One of them is at Chelsea and they also have to play us. So for me, the Premier League is always the biggest test - more than any cup competition.
"It is the same for Liverpool. I don't believe they go into a new season just to focus on the Champions League. Their first target is to win the title.
"It is only when it is no longer possible to win the league that you focus on the rest."