Rice insists neither player should carry blame from a defeat that belongs to the whole group.
Arsenal led through Kai Havertz's sixth-minute strike before Ousmane Dembélé's penalty restored parity. PSG won the shootout with Eze and Gabriel both missing, the latter's effort blazing over the bar to hand the French champions back-to-back European titles.
Rice, speaking to TNT Sports, was clear about where his loyalties lie.
"Devastated to miss a penalty in a Champions League final, obviously it's not nice. But we love them and we're with them. It happens in football. They're not going to be the last players to miss penalties in finals."
He went further.
"Without those two this season we wouldn't have won the Premier League, that's for sure. Gabriel — I've run out of words for him as a person, as a player. Eze has had some huge goals for us this season. It happens. It's football and it's cruel. We take positives and we keep going."
On the broader picture of the campaign, Rice refused to allow a shootout loss to define what Arsenal produced.
"Yeah, it's gutting, it's devastating to lose a Champions League final on penalties. But I'm trying to take perspective on how far we've come as a group. Incredible season, gave it absolutely everything. It's a lottery. It's football. Some of the best teams ever have lost on penalties and we were on the receiving end of that tonight. We win together, we lose together. I'm so proud of these boys."
He also expressed frustration at a potential penalty that was not awarded for a foul on Noni Madueke during the second half.
"I've not seen it back yet. At first glance on the pitch I think he's ahead of Nuno Mendes. I was gutted at the time because I thought the ref would go and have a look but it was not clear enough to be a penalty — I thought it was and so did our staff and bench."
He added a message about the dressing room reaction from Arteta.
"He's gutted, we're all gutted. He spoke about how much he loves us as a group, this season, what we have done, how we've been 100 percent every game and everything that's been thrown at us. This is only the start for us. That's one thing about this group — it won't define us."