The Hammers welcome the LaLiga side to the London Stadium on Friday after losing the first leg 1-0 in Spain last week thanks to a Munir El Haddadi strike.
It has been an impressive European campaign for Moyes' team, and the former Everton and Manchester United manager pointed to how well they have done against some of England's elite in recent times.
West Ham is currently sixth in the Premier League, three points behind fourth-placed Arsenal albeit having played three games more, and has beaten both Liverpool and Chelsea this season.
Ahead of Friday's second leg, Moyes said that fans should be prepared for nerves ahead of a big European game, saying: “[The fans] better get used to it because we're going to have more, that’s the way I look at it, we’re going to have a lot more of these types of games.
"I hope there'll be more in this tournament, and I want us to be challenging near the top of the league. If that is the case, then use this as a steppingstone.
"I think this is what West Ham supporters hoped for when they did move [from Upton Park to the London Stadium].
"I think they hoped for European nights and hoped for opportunities to come to big games against big sides. In some ways, we've done that but for me, I’ve only scratched the surface. I feel as if this can only be the beginning and we have to build on it.
"In nearly all the games we've played in we've given the big teams a run for their money and in the Premier League, we're challenging the top teams and if we can challenge the top teams in the Premier League, then we can give ourselves a chance in other games."
The Hammers' boss also spoke about the emotional scenes on Sunday after Ukraine international Andriy Yarmolenko scored the opener in the 2-1 win over Aston Villa.
Yarmolenko was in tears as he celebrated the goal in light of Russia's invasion of Ukraine.
"It was special, but at the moment I just felt it was us getting one goal in front at the time and it was special for that reason alone because the game was tight, and Aston Villa are a good team," Moyes said.
"We'd not scored as many goals in open play as we'd have liked, so to go in front was important for us. The special part was Yarmolenko scoring.
"It was the first time he has been back after the war began and he came on and made a difference, scoring the goal, which obviously drew a lot of attention for that reason, but hopefully it's drawn attention in different parts of the world as well."