Quinn Priester delivers a pitch in the first inning of the Red Sox’s 3-1 win over the Rays on Sunday in Boston. In his first start for the Red Sox, Preister allowed one run on four hits in five innings. Steven Senne/Associated Press

BOSTON — Vaughn Grissom had an RBI double and scored a run to help Boston beat Tampa Bay 3-1 on Sunday in the teams’ season finales, earning the Red Sox third place ahead of the Rays in the AL East.

The Red Sox finished the season with a record of 81-81, missing the playoffs for the third straight year for the first time since 2010-12. Boston was 78-84 in each of the past two seasons.

“It’s disappointing that we didn’t make it, especially the way the season went the last month and a half, not only with us but around the league,” Red Sox Manager Alex Cora said before the game. “We had a chance.”

The Rays ended the year at 80-82, halting a stretch of five consecutive seasons going to the postseason. They went 99-63 in 2023. It was the Rays’ first losing season since 2017.

“I mean, look, not where we want to be,” Tampa Bay Manager Kevin Cash said. “Know that we’ve got some work to do. I’m confident we will work very hard this offseason and certainly going into spring training to find a way to be playing a little deeper.”

Dylan Carlson had three singles and an RBI for Tampa Bay.

Boston honored longtime radio voice Joe Castiglione with an on-field pregame ceremony. The 74-year-old called his final game Sunday after being the team’s lead radio voice since 1983. He was inducted into the Baseball Hall of Fame this summer with the Ford C. Frick Award.

Before the top of the eighth, the team ran a montage of his calls over highlights shown on the center-field scoreboard. When it was over, the entire Red Sox dugout emptied, with players stepping onto the field, looking up and applauding toward him in the booth behind home plate.

“The players coming out … that would be up there,” he said of what moment touched him the most.

Recalled from Triple-A Worcester before the game, 24-year-old right-hander Quinn Priester (3-6) allowed a run on four hits over five innings in his Red Sox debut. He was acquired from Pittsburgh for minor league infielder Nick Yorke on July 29.

Justin Slaten got the final three outs for his second career save.

Making his 26th start, Rays 27-year-old righty Ryan Pepiot (8-8) gave up two runs, one earned, in four innings. It was his 13th straight start allowing three or fewer runs.

Grissom doubled in the third and scored from third on Triston Casas’ grounder to first, sliding in to make it 2-0.

“It was a long season, I thought we did some great things,” Boston outfielder Jarren Duran said. “We had our bumps in the road. Overall, I thought we had a really good season. We had some young guys, (they) kind of had to learn their bumps in the big leagues, which was good. … I’m just excited with what they’re going to be able to do in the years to come.”

The paid attendance was 34,862, giving the Red Sox a home total of 2,659,949 for the season.

“You reflect on what happened during the season, what happened in the second part of the season,” said Cora of his team going 28-38 since the All-Star break. “It’s going to hit us hard to be honest with you. … It’s a reality. We didn’t play good baseball at the end.”

TRAINER’S ROOM

Red Sox: Cora said after the game that Masataka Yoshida would have an MRI on one of his shoulders Tuesday.