Rice 'knew' Arsenal would dethrone Real Madrid
Rice's two stunning free-kicks in the first leg set the Gunners on their way to dethroning the defending European champions.
The England international also won man of the match in the second leg as goals from Bukayo Saka and Gabriel Martinelli secured a famous win in Spain.
"It's such a special night for this club, it's a historic night for this club. We have an objective in this competition, we want to play the best teams and we want to win this competition," Rice told TNT Sports.
"There was a lot of talk coming here about them coming back because they've done it so many times before.
"But we had so much belief and confidence from that first leg that we could come here and win the game.
"We knew we were going to suffer but we knew we were going to win."
Arsenal will face Paris Saint-Germain in their first Champions League semi-final since 2009.
The London club have never won European football's top prize and last won the Premier League back in 2003/04.
However, Rice, who joined from West Ham for a club record £105 million ($139 million) in 2023, believes major trophies are just around the corner for Mikel Arteta's men.
"It's massive. I sensed before I signed for the club that we were on an upwards trajectory," he added.
"This club is going to do special things in the coming years. We all fully believe in it, we have full trust in this manger - he's unbelievable!
"Semi-finals is massive for us and we want to take tonight in."
Madrid rarely threatened to overturn their first leg deficit but Rice and Arsenal had to survive a scare after he was initially penalised for a foul on Kylian Mbappe inside the penalty area in the first half.
After a lengthy VAR check, the spot-kick was eventually ruled out and a yellow card that would have ruled Rice out of the first leg of the semi-final was rescinded.
"I knew it wasn't a penalty," said Rice. "He just fell to the floor."