Arsenal crashed out of the competition last season when they were beaten in the semis against United.
When asked if United's 3-1 victory at the Emirates was embarrassing for the Gunners, Walcott said: "Of course it was.
"We’ve had disappointments in this competition over the last couple of years – Manchester United in the semis last year. We need to build on results. Hopefully, if it comes to it we’ll learn from our mistakes and try to go one step further.
"We were very disappointed in the games we played [against United]. We want to do something for the fans.
"As long as we win something this year and bring something back for them because they’ve been very patient when we haven’t won anything.
"This year we’ve got a great chance of doing well.
"If we get an English team, it will be like a Premier League battle. We want to go that one step further."