The closest they came to winning the most prestigious club tournament in Europe was in the 2005-06 season, when they lost 2-1 to Barcelona in the finals.
"This drive (to win the competition) is immense. It has never been done at Arsenal and we were very, very, very, close," Wenger told reporters.
"On the other hand, I have been long enough in the job to know you have to be realistic and know that you have to put hard work in," the 65-year-old Frenchman added.
The Gunners were favourites in their round of 16 tie against Ligue 1 side Monaco last season, but were knocked out by the away goals rule after an aggregate score of 3-3.
Wenger wants his side to show they have learnt from their mistakes.
"If we missed one game last year, then it was our home game with Monaco. We were not patient enough and we wanted to make the difference in the first game," Wenger said.
"We know we have some way to put that right, that is a regret of the season last year. We know as well that we can show that we have learnt from that."
Arsenal have to play four away games over the next few weeks, including kicking off their Champions League campaign when they travel to Croatia to face Dinamo Zagreb on Wednesday.
"It is more the global programme we have to absorb in the next three weeks, rather than one game," Wenger said.
"I know the same team cannot play every single game over the next three weeks. I try to keep the balance right and give a little breather to players who need it."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
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