SANTA CLARA, Calif. -- Before the San Francisco 49ers started their latest postseason run, coach Kyle Shanahan sat down with the team's analytics staff and went through the potential scenarios for a game that might reach overtime.

The NFL installed new rules for postseason overtime in March 2022 that would allow for each team to get a possession regardless of what the team with the ball first does (unless there is a defensive score). But the Niners had not been involved in an overtime game in the playoffs in that time.

All of which made what happened in Sunday night's Super Bowl LVIII loss to the Kansas City Chiefs uncharted territory for both teams.

After multiple Niners said after the game they were not aware of the overtime setup, Shanahan said Tuesday he had laid out a plan with his staff before the playoffs began. He said he also instructed his assistant coaches to let the team know before the overtime period started but did not feel the need to discuss that plan with his team before that point.

"We told everyone as we were waiting for the coin toss to review everyone to make sure they're sure before we go out," Shanahan said. "So, we asked position coaches to do that. But I didn't cover it in a meeting on the Super Bowl week. I don't think that changes anything."

Multiple 49ers said Tuesday that whether they knew the specifics of the rule or not did not change the fact that they needed to try to score on offense and get a stop to beat the Chiefs and claim the franchise's long-awaited sixth Lombardi Trophy.

Quarterback Brock Purdy said quarterbacks coach Brian Griese did indeed give him a heads up on the rules at the end of regulation.

"He explained the rules to me and everything so I had an understanding of it," Purdy said.

On the heels of San Francisco's 25-22 loss to the Chiefs, Shanahan's decision to take the ball first after the 49ers won the toss has been scrutinized. The Niners took the ball and managed only a 27-yard field goal from kicker Jake Moody before Chiefs quarterback Patrick Mahomes marched his offense down the field to win it on a 3-yard touchdown pass to receiver Mecole Hardman.

After the game, Shanahan said his discussion with the team's analytics staff had indicated it would be best to take the ball first because if both teams matched scores on their opening drives, the Niners would get the ball to open the portion of overtime in which the first team to score would win.

On Tuesday, Shanahan explained that those discussions took place before the playoffs, but he wanted to remain flexible depending on how the game was playing out. If the game had been more high scoring, Shanahan indicated he might have taken the ball second where he would have known exactly what he needed to win the game before San Francisco's first possession.

"I always make [the decision] in the heat of battle with that information," Shanahan said. "If it was like the Super Bowl the year before the one that seemed more like a shootout, I think I might have felt a little bit differently but having that information going in and the way ours was going, I didn't feel differently. I felt accurate with what they recommended."

Niners general manager John Lynch also pointed out that the 49ers defense had just been on the field trying to fend off Kansas City's frantic final drive. The Chiefs marched 64 yards on 11 plays, and Niners cornerback Deommodore Lenoir and safety Ji'Ayir Brown had to be helped off the field with injuries just three plays before the tying field goal.

"When you're playing Mahomes, you're chasing him a lot," Lynch said. "So, there's a lot of effort that's expended. I think the context from there is you need some time to get fresh. So, all those things play into it. Those are sound decisions."

After their second devastating Super Bowl defeat in four seasons, the 49ers returned to the Bay Area on Monday. They spent Tuesday cleaning out their lockers, discussing the plays they wish they'd made in the game as well as how they plan to spend time grieving the contest -- and championship -- that got away.

Lynch vowed to continue working to improve the roster, acknowledged that the team hopes to re-sign wide receiver Brandon Aiyuk (who has one year left on his rookie deal) and that the team will use their latest loss on the big stage as "fuel" for another crack at it all next season.

A weary Shanahan spent time talking to as many players as possible before they left, noting that he hadn't yet watched the film from the Super Bowl. He said expects his coaching staff back largely intact but that those conversations still have to take place in the coming weeks.

Asked how he feels about the growing perception that he can't win the biggest of games, Shanahan made it clear he isn't worried about outside discussion so much as he can reach the NFL mountaintop.

"If I fixed perception, that means I did everything I wanted to do, which isn't fixed perception, it's winning a damn Super Bowl," Shanahan said. "We've won a lot of big games here. We won a lot of big games to get into the playoffs. ... These two Super Bowls have been tough losing to Kansas City. But to think that if we win that, that means I can win a big game. No, that means our team won a Super Bowl. That's what I understand.

"You guys can have any narrative you want, but the success or the failure, it comes down to one game. And I hope that I can be a part of the team that wins a game at the end of the year. But to say that the Niners can't win a big game would be an extremely inaccurate statement."