Offset language allows teams to recapture guaranteed money if the player is released and signs with another team.
If the Titans give Mariota a contract without offset language, that would allow him to "double dip" and receive payment from another team as well as from the Titans should he not play out his deal.
"We've always had offset language in our player contracts. It's nothing new," Underwood said. "I think it is important where a high first-round draft pick is concerned, because it's the precedent. Everything that we do is precedential for the next round of contracts.
"So keeping the offset in place is something we want to be able to do going forward. And the minute you back away from the contract principle then you no longer are able to assert it going forward."
Underwood said the Titans would be giving up a longstanding principle going forward if they allowed Mariota not to have offset language.
"Whatever you do echoes into eternity with player contracts," he said. "We just can't afford to take a step back, at least this early in the process. We're still a couple of weeks away from training camp."
Speaking about Mariota's contract situation in June, Titans general manager Ruston Webster said: "I don't concern myself too much with it if a guy misses a few days."
Underwood also indicated that while missed time at the start of camp isn't ideal, it also wouldn't be deadly.
The Titans report to camp on July 30 and practice for the first time on July 31.
"Getting a first-round draft pick, a quarterback, signed and in camp on time, it's a big deal," he said. "It's something we need to be focused on. But using that or any other excuse to subvert the negotiating process, that's faulty logic.
"You still need to stick to your guns about what it is you're trying to achieve in the contract negotiation. You may need to use some fallback position. But getting your first-round draft pick to camp on time is important. Sticking to your guns about what you need to get in a contract is also important."
Underwood is not negotiating the contract but said he expects it will be closer to training camp when a deal is finished. He said he assumes the team and Mariota's agents, Bruce and Ryan Tollner, remain in contact, though the debate is over just the offset language.
"My understanding is, that is all that is left," Underwood said. "I'm sure there are tiny odds and ends, but that is all that I'm aware of."
Bruce Tollner didn't immediately return a message seeking comment.
Titans won't budge on Mariota contract language
ESPN Titans reporter Paul Kuharsky discusses what Tennessee CEO Steve Underwood is saying about the team being adamant about an offset clause in quarterback Marcus Mariota's deal and whether it will impact his presence at training camp.