Hudson-Odoi was injured in Chelsea's Premier League match against Burnley a month ago, with the winger, and Loftus-Cheek becoming become the first academy players to start four league games in a row since John Terry.
The pair had to fight hard all season and used the Europa League as a springboard to convince a stubborn Maurizio Sarri to change his line up.
After Hudson-Odoi's injury, Loftus-Cheek was hurt in a post-season charity match against New England Revolution in Boston, USA, with his injury similar to the young winger and both could be out for up to nine months.
However, their contribution has not been forgotten and Azpilicueta has urged the Blues to beat Arsenal in Baku on Wednesday so the pair can have their first taste of European silverware.
"Yes, it is an extra motivation for us," Azpilicueta said of winning for the injured duo. "Both of them were very unfortunate with their injuries. They were both in their best moment of the season, playing regularly and were important for the team.
"So it was a huge downer for all of us, including them. All of us will take it as an extra motivation to win it for them because they have been very important to get us to Baku. They deserve us to give everything for them. Hopefully, we can do it."
Azpilicueta's first trophy for Chelsea was the 2013 Europa League where he featured heavily after his £7 million ($9m) move from Marseille.
That trophy proved a springboard for better things and he is encouraging his young team-mates like Kepa Arrizabalaga, Ross Barkley, Andreas Christensen and Emerson Palmieri to taste success and build on it.
"That was my first final with Chelsea when I was 23 years old," he added. "The stage is different when you’ve experienced those kinds of games. I’ve got that in my backpack and it will help me hopefully in Baku.
"I’ve had a couple of experiences winning trophies, playing in finals, and obviously that helps the other people as well. Having a few of us that have played regularly in big games is important to help your team-mates. A couple of players never played in a European final.
"We have to work together because it’s a big game, it’s a derby, and hopefully we can win it. When you play your first final you don’t have the experience of those kinds of games, and sometimes the small details can make the difference. We have to be ready to be focused.
"Every team is prepared for it and we have to be ready. Honestly, with a trophy in the middle, it doesn’t matter who you play. You want to win it. Arsenal is a derby, we know it’s a big game, and that gives us an extra feeling, but every time you play a final you want to be a winner.
"It doesn’t matter who you’re facing. When we started the season we wanted to get into every trophy possible and to get into the Champions League. We did it through the top four, but when we started our first game in Greece, we were targeting Baku and trying to get the trophy."
Gary Cahill will bow out of Stamford Bridge after the game in Azerbaijan and he is a player who has won every major honour in his time at the club.
He remains club captain but Azpilicueta has taken over those duties this season on the pitch, as Cahill has struggled to convince manager Maurizio Sarri of his worth.
Azpilicueta says the pair haven't discussed who will lift the trophy, should they win it, and he thinks it will be decided in the moment.
"I don't know [what we will do]! First, let's win it and then we will see."