The 16-year-old started alongside Charlie Lindsay in midfield for David McCallum’s men as a late second half surge secured all three points for the Light Blues.
Speaking exclusively to RangersTV after the win, Rice commented: "It’s brilliant [to make the step up to the B team]. I’m still young and learning.
"Playing alongside Charlie, he is a is a bit older and more experienced, he’s played in these sorts of games. He helps you through the game.
"I’m looking forward to [the Liverpool game] now. We’ll have a good couple of days training and go again."
Edinburgh University brought the game back on level terms midway through the second half and, although the Light Blues responded to prevail with the victory, the young midfielder says there is always room for improvement.
He continued: "We knew that from the start [that patience was required]. They were going to come and make it difficult defensively. We did well in the first half, broke them down and created chances, but we didn’t take them and need to be more clinical. Then in the second half they go up and score.
"We came out in the first half, looking to go again and get a couple of goals. We concede a goal and our heads dropped then made it hard for ourselves. It’s always good to get the three points, but it wasn’t up to our standards. We’ve got a big game on Wednesday so we go again."
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