The Celtics have become known as one of the league’s more aggressive franchises, collecting assets and making trades at a sometimes dizzying rate. And so as Thursday night’s NBA Draft approached and team executives made it clear they would actively attempt to make moves, there was a sense that anything was possible.

The Celtics entered the night with the 16th, 28th, 33d, and 45th overall picks. They said they wanted to move up and acquire a higher pick, and they said they did not want to use all four selections.

But all trades demand partners, and sometimes that can make things quite murky. Ultimately, president of basketball operations Danny Ainge said, “the price was way too high.”

And so the Celtics stayed on the schedule that few thought they would stay on, using all four picks. The team selected Louisville guard Terry Rozier (16th), Georgia State guard R.J. Hunter (28th), Louisiana State forward Jordan Mickey (33d), and William & Mary guard Marcus Thornton (45th).

“We tried hard,” Ainge said. “We tried hard to trade up. We spent the last couple of weeks trying to move up, and really today was the only time we had any indication we could move up. But we were trying.”

When it was pointed out to Ainge that he appeared frustrated as he stood at the dais here in the Seaport Hotel as the night neared its conclusion, he said that was inaccurate. He said he was simply tired.

“At the end of the day,” Ainge said, “it’s like Red [Auerbach] used to say: ‘Sometimes the best trades you make are the ones you don’t make.’ ”

Danny Ainge says the Celtics tried hard to trade up

If there was any disappointment among the Celtics’ brass regarding the inability to make a move, it was tempered by the enthusiasm about what the team believes can be a strong four-player crop.

Rozier was having his draft party in Cleveland on Thursday night and had received no indication when he would be selected. Then he saw commissioner Adam Silver walk onto the stage at the Barclays Center in New York and found out with the rest of America that he had been selected by the Celtics.

Rozier was enjoying the moment with friends and family at a local club, and about 10 minutes after he was picked he jumped into a swimming pool with his cousin and brother — while still wearing a suit — to celebrate.

“Man, it’s amazing,” the 6-foot-2-inch, 190-pound guard told the Globe by phone. “Just to get this opportunity, not even just getting picked this high, but getting picked by a guy like Danny Ainge, I don’t want to let him down. This is amazing.”

Brad Stevens on the Celtics first round picks

Celtics coach Brad Stevens praised Rozier’s grit and toughness, and Rozier’s coach at Louisville, Rick Pitino, said Rozier would thrive in Boston.

“He’s just scratching his potential,” Pitino said by phone. “We had the poorest shooting team I’ve had in some time [this season]. Defenses packed it in against him, and he still got in the lane and did great things for us.”

Rozier averaged 17.1 points, 5.6 rebounds, 3 assists, and 2 steals in 35 minutes per game for the Cardinals last season, his sophomore campaign.

Hunter, a 6-6 guard with excellent shooting range, averaged 19.7 points per game as a junior.

“I think he’s got a big upside,” Stevens said. “He really shoots the ball.”

The 6-8 Mickey is slightly undersized at his position, but is a good athlete and a dynamic shot-blocker. Ainge said he immediately becomes the most athletic player in the team’s frontcourt.

Thornton, who averaged 20 points per game for William & Mary as a senior, was the Colonial Athletic Association’s player of the year.

Chris Gasper and Gary Washburn on the Celtics Draft

Ainge acknowledged that it was unlikely that the Celtics would have all four new players on their roster next season. He suggested the possibility of at least one pick playing overseas next year, which would not cost the Celtics a roster spot.

The additions of Rozier and Hunter — who receive guaranteed contracts as first-round picks — make a crowded young backcourt even more congested. The team returns starting guards Avery Bradley and Marcus Smart, and arguably its best player — Isaiah Thomas — comes off the bench.

“Obviously we have a lot of guards, and we’ll figure it out,” Ainge said. “I like them all. We may have to make some tough choices, but we really like all the guys.”

Ainge has said the Celtics would draft the best available player before they considered need, mostly because rosters are so fluid. And Stevens said he believes the members of this deep backcourt can coexist.

“You hope they can complement each other in a kind of positionless way,” Stevens said. “But at the same time, there’s certainly going to be a lot of competition. There’s no question about that.”

Hunter, like Rozier, is thrilled for this new opportunity.

“Unbelievable,” he said. “Especially the Celtics, anybody who’s ever watched basketball knows that tradition. I’m excited, man. Talented team, great young coach and organization. I’m beyond excited.”

Adam Himmelsbach can be reached at [email protected].