The first three preseason games that featured fractured lineups and produced uneven competition were more about evaluating personnel than generating results. That is a good thing given the Rangers lost all three while being outscored by an aggregate 12-6 by the Devils (twice) and Flyers.

It is never a good thing, however, to be as disjointed and disconnected as the Blueshirts through most of the three contests, with and without the puck. And most certainly not when these types of breakdowns were an epidemic the second half of last season.

Which is why, after a day off on Sunday (as opposed to the preceding off-nights in Philadelphia and New Jersey, respectively), the Rangers focused a fair amount on cleaning up their approach when they reconvened for Monday’s split-squad sessions.

“We talked about it,” said Henrik Lundqvist, scheduled to play half of Tuesday night’s Garden match against the Islanders. “If you look at the lineups, especially the two games on the road, there was a pretty big disparity, but being disciplined with the puck is something we’re going to want to pay attention to the next three [exhibition] games.

“We definitely have the skill to make plays and be able to make the difference in games, but the key for us is going to be puck management and knowing when and how to use that skill and when not to just rely on talent but instead rely on our structure. That’s what you need to be able to do in the critical moments.

“Well, all game, really, but it comes down to making the right play in the big moment. Having skill is very important, but so is being smart.”

David Quinn said his team had yielded eight five-on-five scoring chances off defensive-zone coverage but 27 off the rush. The first represents an acceptable total. The other, though, signifies something quite different.

“Guys are trying to do too much,” the coach said. “Some guys are trying to do too much to make the roster and other guys that think they’re on the roster are trying to do too much to crawl up the roster. That’s not what we’re looking for.

“We’re looking for people to do things that will allow us to have success collectively and play winning hockey. We certainly haven’t had enough of that the last two games.”

Asked whether 20-year-old Filip Chytil should be considered an incumbent or whether he needs to earn a spot on the opening roster after doing so both as an 18-year-old and 19-year-old, Quinn said, “He needs to make the team.”

When asked where No. 72 stood at this juncture, the coach said, “He’s in the process of making the team.”

Brendan Lemieux, who had been nursing a tender groin, is set for his pre-season debut on Tuesday. … Marc Staal is scheduled to skate on the left with Adam Fox. … Brett Howden will skate between Vitali Kravtsov on the left and Kaapo Kakko on the right while the team’s presumptive first line of Artemi Panarin-Mika Zibanejad-Pavel Buchnevich debuts. … The presumptive first defense pair of Brady Skjei-Jacob Trouba will skate together for a third game.