Dave Moyes’ side overturned a 1-0 first-leg deficit against the six-time winners by winning 2-0 in extra time last night with a standout performance here at the London Stadium.
The Hammers were waiting this morning to find out their opponents in today’s quarter-final draw.
But Rice said, “There’s no one to worry about. Sevilla were probably the favourites. When the draw happened, people thought we would be eliminated, and we eliminated them.
“We can go anywhere and get a result. Teams come here knowing they’re ready for a game.
“[It was] so special last night. This club, the stadium, the fans, the players, we deserve these great European evenings. We stepped up.
“We worked hard for this. Relegation battles, since the arrival of Moyes. Still up there in the Premier League and now in the quarter-finals. There is a big buzz around the place.
“The manager deserves massive credit. When he arrived, we weren’t playing as a team. Before the game, he gave a great speech, a motivational speech, which really stimulated us. I am at a loss for words. Just walk the field at the end, figure it all out. Everything about the night was so, so special.
Michail Antonio recovered from a hamstring injury picked up on Sunday to start. He claimed an assist for the opener and caused problems for the Sevilla defense throughout, playing almost all 120 minutes.
“We don’t fear anyone,” Antonio said. “We play in the Premier League and it doesn’t matter who we play against, we try to get three points. We’re here to win it. We’re not just here to participate. Why can’t we win it? This season is like a dream come true. It’s the first time in Europe for me. I became West Ham’s top scorer in the Premier League.
“We dominated. We have always believed in ourselves. From the first half we were on them, creating chances.
Tomas Soucek equalized West Ham on aggregate with a superb first-half header through Antonio’s cross.
West Ham dominated but needed extra time to seal their place in the last eight.
Andriy Yarmolenko was at the heart of another emotional moment as the Ukraine international netted the winner after Pablo Fornals’ shot was knocked down. The goal came just days after Yarmolenko scored in the opener against Aston Villa, his first game since Russia invaded Ukraine.
“Yarmolenko was a little emotional away from the guys afterwards,” Rice said. “For what he went through to play like that, it’s all to his credit – his desire, the way he chased players and scored two crucial goals. He deserves it. He stepped up. I’m delighted for him.
Moyes has never passed a quarter-final in European football.
The manager said: “It’s great but I have to go further now, that’s my big thing. I challenge the players but I also have to challenge myself and find a way to get a result in the next one. match.