McGloin tweeted that the penalties announced by the NCAA on Monday were "extremely harsh."
"I am a Nittany Lion and will remain one," he also tweeted. "I believe in the core values I have learned in this program. It is not Nittany Lion Football. It is Nittany Lion family."
McGloin's tweet was followed later Wednesday morning by a statement from the Penn State football program, which it released on its Twitter account @PennStateFball:
"This team is sticking together. We aren't going anywhere. And we could not be more proud to be Penn Staters now. We look at this as a great opportunity to have the ability to bring back not only a team but an entire university.
"This team has taken on more adversity than any team has faced in history, which is a testament to our commitment to our team's character, our fans, and our university. One man didn't build this program, and one man sure as hell cannot tear it down. This program was built on the backs of the thousands of great men who put on the Penn State uniform. Today it is no different.
"No sanction or politician can tear this team apart. No one can take away what this university means to us. We will stick together and create our own legacy. Our loyalty lies only with our teammates, coaches, fans and families. No one else.
"It's not going to be easy, but we know that we have acquired the strength that we have overcome, and we will embrace our anger and burn it as fuel this season.
"We can't wait for Sept. 1 and to be back in Beaver Stadium and playing for Penn State in front of the best fans in the nation. We ask everyone to come out, show the support, wear your colors proudly and show that adversity makes the Penn State nation tougher and stronger."
In addition, more than 30 Penn State football players held a news conference Wednesday to say they are staying in Happy Valley despite the NCAA sanctions that will keep their team out of a bowl game for the rest of their careers.
Flanked by more than two dozen teammates, seniors Michael Mauti and Michael Zordich vowed to restore Penn State to greatness after an unprecedented child sex abuse scandal that shattered the program's image as a place where "success with honor" was the rule.
"We want to let the nation know that we're proud of who we are," Zordich said Wednesday. "We're the true Penn Staters, and we're going to stick together through this. We're going to see this thing through, and we're going to do everything we can for the university. We know it's not going to be easy, but we know what we're made of."
Neither Zordich nor Mauti -- both sons of former Penn State players -- mentioned former assistant coach Jerry Sandusky by name.
"We take this as an opportunity to create our own legacy," Mauti said. "This program was not built by one man and it's sure as hell not going to get torn down by one man. This program was built on every alumni, every single player that came before us, built on their backs."
Besides McGloin, several Penn State players tweeted their allegiance to the school on Wednesday, including senior cornerback Stephon Morris, who tweeted: "I'm not going anywhere We Are Penn State forever. That's final!! Love this University, more important I bleed Blue & White!!"
As part of the NCAA's Monday ruling that dealt the school a $60 million sanction, a four-year football postseason ban and a vacation of all wins dating to 1998, Penn State players are allowed by the NCAA to transfer to another school without sitting out a year.
McGloin, a former walk-on, was given the starting job last month by coach Bill O'Brien.
He completed just 54 percent of his passes last season, and missed the TicketCity Bowl versus Houston -- a 30-14 loss -- after sustaining a concussion in a locker-room scuffle with a teammate.
Information from The Associated Press was used in this report.