Rice supplied the assist for Kai Havertz's decisive 16th-minute goal, delivering the cross that allowed the German forward to finish at the far post. He was subsequently named player of the match after an influential display as Arsenal moved three points clear at the top of the Premier League.
The result also represented a significant milestone for Mikel Arteta's side, who had not won a league fixture at Anfield since 2012.
"Coming to Anfield, I think the record here speaks for itself – the first win here in 14 years – so today to win 1-0, to show that togetherness, resilience – it's unbelievable," Rice said.
"I'm just delighted to get the win and the three points."
The midfielder revealed that Arteta had made the long wait for victory at Anfield a central part of his preparation, using previous away successes to reinforce the importance of approaching the match with the right mentality.
"The manager drilled that into us, showed us the last time before we won at Spurs away, Chelsea away, it was many, many years, and Liverpool was the longest outstanding one. He drilled it into us to have that mentality to come here today and win, to show that togetherness.
"I think the togetherness is unmatched. I've never been in a team like it that's got this togetherness. The manager, what he's built, how happy everyone is every day to come in, see each other, work and represent this club – it's amazing."
Rice was also pleased with his own contribution, particularly after previous difficult experiences at Anfield. His assist proved decisive, but his work across midfield was equally important as Arsenal came under pressure from the hosts.
"Yeah delighted because this Liverpool team has so much quality. I've been on the end of some big results here before, so to come and win today, put in a really good performance against a top side who are doing really, really well, I'm delighted."
Arsenal's victory was also a response to their League Cup defeat to Fleetwood earlier in the week, which Rice acknowledged had been a difficult result for the squad to absorb.
"After Tuesday it felt like the world had come crashing down, losing to Fleetwood, but then to have the reaction like this – that's the beauty of football. You always have one the week after to put things right, and we've done that today and made Arsenal fans very happy. So, bring on Wednesday."
For Rice, the performance demonstrated the strength of the collective effort Arteta has built at the club. Arsenal left Anfield with more than three points: they had overcome one of their longest-standing away challenges and strengthened their position at the summit.