Red Sox reliever Cam Booser reacts after giving up a grand slam in the seventh inning to Aaron Judge in the Red Sox’s 5-4 loss to the Yankees on Friday in New York. Adam Hunger/Associated Press

For the past few weeks the Boston Red Sox have managed to stay on the periphery of the playoff race. They didn’t really play well enough to stay in the hunt, but the teams ahead of them played so poorly there remained a slight hope.

Hope was lost over the weekend in New York. The Sox lost 3 of 4 to the Yankees and arrived in Tampa Bay 4 1/2 games out with 12 remaining.

Making matters worse is that both the Tigers and Mariners have won 7 of 10 games to move two games ahead of the Red Sox in the race for the final wild-card spot. Not only are the Sox facing overwhelming odds to catch Minnesota, but they would have to leapfrog two teams to do it.

After 150 games the Sox are 75-75, a .500 team in every way. Like most AL teams, they are a flawed unit, and the flaws were too much to overcome.

It’s extraordinarily difficult to make the postseason when you have the most errors and most unearned runs in the major leagues, as well as the highest ERA and most blown saves since the All-Star break.

We saw glimpses of hope along the way: a starting rotation that has been one of the best in the majors over the last month and an offense that featured breakout seasons by several young players.

Manager Alex Cora was hoping Saturday’s 7-1 win over the Yankees would serve as a springboard for a stretch run that would beat the odds. He was visibly upset after Gerrit Cole hit Rafael Devers in the first inning. Three innings later Cole intentionally walked Devers with no one on base, an extremely rare move.

The decision backfired on Cole, who had a no-hitter going when he walked Devers with one out in the fourth. Eleven batters later he was out of the game after allowing seven runs.

It was a stirring win, but after the game Cora and the Sox were still unhappy because they felt Cole intentionally hit Devers.

“If (making the postseason) happens, we’re going to look back at yesterday and we’re probably going to thank Gerrit Cole (for getting) us going, to be honest with you,” Cora said before the series finale Sunday.

Instead, Aaron Judge hit his second home run of the series in the third inning and the Sox were beaten, 5-2. It was the second homer in the game allowed by Kutter Crawford, who has given up a major league-leading 33 this season. That’s tied for ninth-most in Red Sox history.

Kutter Crawford gets a new ball from catcher Danny Jansen during the Red Sox’s 5-2 loss to the Yankees on Sunday in New York. Crawford gave up two home runs and has allowed a league-leading 33 this season. Adam Hunger/Associated Press

Yet Crawford was a bright spot this season, showing he can handle the workload as a big-league starter and giving the Sox rotation the type of depth it needs to contend in the future.

These last two weeks, we will see who can be part of the mix next year. Starter Richard Fitts has pitched 10 2/3 innings since his call-up and has yet to give up an earned run. Can he be a starter next year?

Zach Penrod has made two relief appearances, a former independent league fringe player who has shown the velocity and tenacity to succeed in relief. He has also not given up an earned run.

The bullpen will need an overhaul, and pitchers like Penrod will get a chance to be part of it. While the Red Sox have blown more saves than any other team over the second half, they’ve also had the most save opportunities in the AL. They’ve had their chances.

Boston is mathematically still alive. Several teams have gone on runs in the final two weeks and stunned baseball by qualifying for the playoffs. But this team has just one winning streak of three or more games since July 5. In the end it just didn’t have enough to catch up to the other flawed teams in the American League playoff race.

Tom Caron is a studio host for the Red Sox broadcast on NESN.