UEFA's second-tier competition, formerly known as the UEFA Cup, is the only major prize to elude United's grasp, but they have an opportunity to add it to a bulging Old Trafford trophy cabinet this season.
Jose Mourinho's team face Celta Vigo away on Thursday in the first leg of the semi-final, with more than just silverware at stake for the four teams remaining in the tournament.
"Winning this competition would give us the ticket to the Champions League, it's true," Valencia told a news conference.
"But the most important thing for us is that United doesn't have this trophy yet. We're definitely concentrated and focused for this match."
Mourinho has made a point of bemoaning his team's recent injury problems, which have been compounded by a congested fixture list.
Defenders Phil Jones and Chris Smalling are nearing a return, but Valencia appears to agree with his manager's assessment of the team being hampered by fitness problems.
"We're not the favourites, but we're United and that's a responsibility that we bear," he said. "We have to demonstrate who we are and show it.
"It's been a long competition and thankfully we recovered two of the defenders and Juan Mata is back, so it's been very good for us.
"We know they're a strong team, they haven't lost the last five or six matches in this competition.
"We expect it to be a good match and we want to get a good result from it."
Mourinho described Valencia, converted from a winger to a more defensive role during his time at Old Trafford, as the best right-back in Europe earlier this year.
And while the 31-year-old does not agree with the label, the experienced Ecuador international was flattered by the praise.
"First of all I only have words of thanks to Mourinho for those words," he said.
"I don't consider myself the best, I just want to work hard for the team, but he's given me the confidence to do that, not only me but the rest of the team.
"I hope to give some of that trust back to Mourinho by playing a good match."