Brady was asked Wednesday about his first week with his still-unnamed baby boy with wife Gisele Bunchchen.
"It's good. It's good. I'm glad it's over," Brady said. "Trying to get back to my normal sleep schedule, which I'm sure, for all of us parents, is a little tough early, but it's coming getting used to this."
Brady has finger and rib injuries as well as a sore shoulder.
Last week, Brady sat out practices last Wednesday and Thursday, practiced Friday and started in Sunday's game against the Carolina Panthers.
If Warren and Wilfork can't play this Sunday against the Buffalo Bills, it could cause more problems for a New England defensive line that hasn't shown much of a pass rush.
"If guys go down, another guy has to step in," Warren said. "That's why everybody has to know every position up there on the field."
Warren said playing nose tackle is what Wilfork "was born to do."
"And he does it well," said Warren, who went to the sidelines with an ankle injury soon after Wilfork left for the second time.
"It's something that I think every team -- most teams anyway, if not every team -- goes through at this time of year," he said. "You see a lot of players going on injured reserve and you see a lot of other players get signed to replace them, whether it's off the practice squad, which is usually where they come from, or wherever else they get signed, and it's definitely a concern."
Titus Adams, signed from the practice squad last week, replaced Wilfork against Carolina and made two tackles. Mike Wright filled in for Warren. The other regular starter on the defensive line, end Jarvis Green, has played three games since missing three with a knee injury.
"The whole defensive line, whether it be Myron Pryor, whether it be Ron Brace, whether it be Mike Wright, I mean, all those guys learn multiple positions," Patriots defensive coordinator Dean Pees said.
"We felt like in the last couple games, maybe some of the execution might have been the result of not practicing things enough or not reacting quite quickly enough," he said. "So we tried to simplify it a little bit so there would be a little less decision-making."
"I never want to see any of the starters at any position, or really anybody on the entire defense, get nicked up or walk off the field that way," Pees said. "But hey, that's part of the game."
The Associated Press contributed to this report.