"Minus our record, we're a really good football team," Hyde said. "Next year we're going to win the Super Bowl."
He added: "I feel we've got a chance to go the Super Bowl next year, and I don't want to go to another team."
Hyde scored a six-yard touchdown in the fourth quarter, which ended up being the game-winning score, and racked up 73 total yards in the contest.
Although the win only moved the 49ers' record to 5-10, well out of postseason contention, they are 4-0 since Jimmy Garoppolo took over as the starting quarterback. His strong play since arriving in a trade with the New England Patriots has started to raise the team's expectations for 2018.
Tim Kawakami of The Athletic noted Garoppolo said "I'll talk to him about that" when told about the rusher's bold Super Bowl prediction.
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Whether Hyde will be part of San Francisco's roster next year is unclear.
In October, Benjamin Allbright of Mile High Sports Radio reported the Niners "received and made calls" about the 26-year-old running back before the NFL trade deadline.
San Francisco head coach Kyle Shanahan downplayed the rumors at the time.
"That is absolutely, absolutely 100 percent false," he told reporters. "There is nothing true about that."
Nevertheless, Hyde has ceded playing time to backup Matt Breida, who had 82 yards from scrimmage and a touchdown against the Jags, throughout the season.
Elevating Breida to a more prominent role and drafting another running back in the middle rounds would likely represent a more cost-effective backfield for the 49ers in 2018.