The West Ham player, 22, said he had seen Southgate’s miss, which led to England’s exit in a shootout against the eventual winners.
“I’ve obviously seen that one from the past,” said Rice. “Yes, it’s tough. I’m sure Gareth is going to want to get his own revenge in that aspect as well.
“Obviously he missed a penalty but everyone’s missed a penalty. I missed one two days before the end of the season.
“That’s football. But for Gareth I’m sure he’s ready and of course he’s going to set us up for us to go out there and win and I hope we can do it for him as well so he can get his own revenge.”
Rice admitted that as a Chelsea youth player he had missed three penalties to win three different tournaments but said he had learned and was prepared to step up if called upon.
“It’s just about that process in my head,” he said. “When the ref blows his whistle you don’t have to go. Just give yourself those extra couple of seconds, breathing techniques just to relax yourself then it’s all about visualisation.
“How are you going to put the ball in the back of the net? They’re things I’ve started to develop as I’ve got older.”
Rice, who started all three of England’s group games, said he had deleted his Twitter account so he could focus fully on Euro 2020, with the last-16 match against Germany taking place at Wembley on Tuesday.
“I like Twitter, I’m like a fan, I read stuff but for this tournament it was just best to come off it and focus fully on the tournament and myself,” he said.
“Sometimes you can read things and it puts doubts in your mind about our ability but I had to come off it.”
And he said England were fully focused on the task in hand despite swirling speculation over the club futures of players including Jack Grealish, Jadon Sancho and captain Harry Kane.
“There is speculation about players going but the main focus is at the moment, the country, trying to win this tournament,” he said. “I think if players want to have a move or if players want to move on that can be done and dealt with after the tournament.”