OAKLAND -- As the Yankees mulled over their series-opening 2-1 loss to the A's Tuesday evening at the Coliseum, they circled back to one idea multiple times: the lofty expectations that accompany life as the vaunted Bronx Bombers.

So far in June, they have fallen short of those expectations -- and they're well aware.

"We know we have a higher standard and expect more and know we're going to be better, but we're going through it right now a little bit," manager Aaron Boone said. "Overall this month, we've had a few guys that have gone through some struggles, but I wouldn't call it frustration. I'd call it, like, this is get-to-work time, and how do we get guys going -- and that's on all of us."

New York's lone run of the contest came by way of Josh Donaldson, who returned to the starting lineup for the first time since Thursday. The veteran third baseman blasted a no-doubter to left field that traveled a Statcast-projected 423 feet at 110.8 mph off the bat in his second at-bat, cutting the A's lead to one run in the fifth inning.

Donaldson has struggled early on in the season, slashing .132/.200/.441 through 22 games. He missed close to two months with a right hamstring strain and has scuffled at the plate since his return, leading to Boone's decision to sit him during last weekend's series against the Rangers.

Along with Tuesday's homer, Donaldson made hard contact in his first at-bat, a flyout to deep right-center, but he struck out looking the final two times he came to the plate.

"For the better part since I've been back, I've felt pretty good at the plate," Donaldson said. "I had a few days' stretch, I think last week or something, where I felt a little bit off. I was able to put some work in. ¡­ I felt pretty good with the approach. I think I was able to put a barrel on two balls today, and the other two ABs, guys made good pitches."

Donaldson does not have enough at-bats to qualify on batting leaderboards, but the -0.098 differential between his expected batting average (.223) and his actual batting average (.125) that he carried into Tuesday is the largest in the Majors for batters who have put a minimum of 45 balls in play.

The one thing that has consistently gone right for Donaldson is his power stroke; seven of his nine hits are home runs. But the Yankees are somehow 0-6 when he goes deep.

"The balls that I put in play that aren't going out of the yard are finding gloves," he said. "At the end of the day, I feel like what I can control is how I go about my at-bat, the process of the at-bat and trying to make those adjustments to where I feel like I've been in good positions to hit."

Added Boone: "Hopefully it is something that kind of jumpstarts him this week a little bit. But you know, we've all got to pull our weight and get it going a little more offensively."

New York's struggles at the plate in June, which largely coincide with Aaron Judge's stint on the injured list, persisted.

The Yankees have had difficulties plating runs this month, and even against the A's -- who entered the day with a staggering minus-224 run differential that ranked last in the Majors -- they could not get much offense going.

Oakland's Paul Blackburn, who punched out five Yankees, combined with three relievers to hold the Bombers to one run on seven hits and three walks. New York went 0-for-5 with runners in scoring position and left eight on base.

The Yankees' .196 batting average, .257 on-base percentage and .621 OPS this month all rank last in the Majors. Those numbers would be disappointing for any big league lineup, but they know they're capable of more.

"If you ask anyone, we expect a lot of ourselves," said Anthony Volpe, who had the first three-hit game of his career. "At the end of the day, that's all that matters, because our expectations of ourselves, I think, are going to be higher than anyone can put on us. We're not living up to that, and we know our potential. It's obviously frustrating."

He paused, then continued: "I don't think that discourages anyone; I think it motivates everyone."