Smith will seek treatment following his arrest Friday for suspicion of driving under the influence. After Sunday's loss to the Colts, Smith apologized and acknowledged he will get help, but didn't field questions.
"First off, I wanted to apologize to the team, the organization, my family and everybody I let down," he said. "I also wanted to let it be known that this is a problem and it's something that I will get fixed, and that I'll do everything in my power to make sure that this never happens again.
"I also wanted to let everybody know that once again I'm sorry."
Smith started for San Francisco and had five tackles in a 27-7 loss, two days after he was arrested and jailed early Friday morning following an accident in which his truck hit a tree. York defended the organization's decision to play Smith.
"Our opinion is if you're sitting someone down and paying them to sit down when they're going to seek treatment in the future, we didn't feel like that was an appropriate punishment," he said. "We're not trying to circumvent what the NFL will do. This is about making sure that Aldon has the opportunity to work on something, to get better, and he knows that he has our support and hopefully he has everybody's support in something that is going to be very difficult."
League officials confirmed to ESPN that under the collective bargaining agreement and the league's substance-abuse policy, the 49ers could not suspend Smith. Even though commissioner Roger Goodell has emphatically stressed that DUI violations are high-level concerns, he also cannot suspend Smith under the personal conduct policy because the most recent case still must be adjudicated.
Therefore, Smith's well-being is taking priority before any punitive measures are enforced.
York expects Smith to get help, but the 49ers won't interfere.
"I think Aldon is going to take steps on his own," York said. "We're not worried about that."
Smith is a key pass-rusher and sacks leader for the 49ers, and coach Jim Harbaugh had said leading up to Sunday that the NFL would decide how to punish the third-year pro, who turns 24 Wednesday. He had a franchise-record 19½ sacks last season, second in the NFL.
When asked about Smith getting help, Harbaugh said, "There's a process there we'll apprise you of at the appropriate time."
"It will be indefinite," York said. "There's no timetable."
York said Harbaugh and general manager Trent Baalke handled the situation and communicated with Smith.
"I think this was the best thing for Aldon," York said. "Again, there's no right answer here. We're very fortunate that nobody got hurt, Aldon included and anybody else. And we want to make sure that Aldon is never in a position like this again."
Smith has had a rash of run-ins with the law that raised questions about his character.
"It was disappointing, but we support him, and knowing that what he wants to do is not a one-day fix, it's a long-term fix for Aldon," York said. "Aldon is willing to fight for himself and try to make this right, and I will see it through, and I will support him. I will take any shots that anybody wants to direct at the organization. They can direct at me, and I will support Aldon as long as he is willing to work at this and fight to get better."
Earlier this month, a lawsuit was filed in Santa Clara County Superior Court naming Smith by a Northern California man who said he was shot at a party at Smith's house on June 29, 2012.
The players charged a $10 admission and $5 per drink, the lawsuit said. Smith and former 49ers tight end Delanie Walker, 29, were allegedly intoxicated on Smith's balcony when they later fired gunshots in the air while trying to end the party, the lawsuit said.
Before the 2012 home opener last September, Smith was the passenger in a car accident in Santa Clara County in which the driver swerved to avoid hitting a deer. Smith sustained a cut beneath his right eyebrow. He apologized and insisted he had grown up.
The 49ers selected Smith seventh overall in the first round of the 2011 draft out of Missouri. He became an instant impact player like many of the others chosen by Baalke in the past three drafts.
"This was not an easy weekend for us," York said. "Again, I'll support our players as long as they're willing to work toward getting better and being better teammates, better members of the community. I believe that Aldon wants to do that, and I will support him and I will stand by him as long as that's what he's willing to do."
Information from ESPN senior NFL analyst Chris Mortensen and The Associated Press was used in this report.