But that has certainly been the case, and it was evident again this week during a four-game sweep at the hands of the Yankees, who were without stars such as Derek Jeter, Alex Rodriguez, Mark Teixeira and Curtis Granderson.
Making his second big league start in Thursday's series finale, Kyle Gibson struggled en route to the Twins' 9-5 Independence Day loss at Target Field.
With the loss, Minnesota fell to 23-70 against New York, including the playoffs, since Gardenhire took over as manager in 2002.
"I don't know -- I wish we had answers for all that stuff and why they play so well here," Gardenhire said. "But they've got great players, and they've always had great players since I took over as manager. And great players do good things. Even when they're hurt, they know how to win. Even those kids playing for them know how to win ballgames and got big hits."
Gibson -- who pitched well enough to earn the win in his debut, against the Royals on Saturday -- couldn't replicate his success against the Yankees. The right-hander gave up eight runs on 11 hits and a walk over 5 1/3 innings.
The eight earned runs were the most allowed in the professional career of the highly touted Gibson, who spent four seasons in the Minor Leagues before last week's callup.
"I went back and took a look at all the hits I gave up, and only four were well located," Gibson said. "Coming into this whole experience, I knew if I left pitches up, I was going to get hurt. The first and third inning, mainly, I left a lot of balls up."
The loss spoiled a two-homer effort by Justin Morneau, who recorded his first multihomer game since Sept. 9, 2012, against Cleveland. It was interesting timing for Morneau, who is a candidate to be traded before the July 31 non-waiver Trade Deadline while the Yankees are reportedly in the market for a first baseman.
"My swing is starting to feel more like my swing," Morneau said. "Today, it unfortunately comes in a loss, but hopefully it's a sign of good things to come."
The Yankees jumped all over Gibson early, scoring three runs in the first inning. Ichiro Suzuki led off the game with a double and came around to score on a sacrifice fly from Robinson Cano before Vernon Wells brought home two runs with a single to left.
Wells did more damage in the third, doubling home Travis Hafner before scoring on a single to left from Luis Cruz.
It was more of the same in the sixth, when New York tacked on four runs, three of which were charged to Gibson. Alberto Gonzalez brought home the first run on a single to right field after Lyle Overbay led off the frame with a walk and Cruz followed with a double. Gibson finally recorded an out when Austin Romine hit a soft grounder to second baseman Brian Dozier, who was able to throw out Cruz at home.
Left-hander Brian Duensing came on in relief of Gibson and promptly served up a two-run triple to Ichiro. Ichiro then scored on a groundout by Zoilo Almonte, with the run charged to Duensing. Ichiro finished a home run short of the cycle.
"It seemed like he made some mistakes," Yankees manager Joe Girardi said of Gibson. "The young man has pretty good stuff, from watching him pitch his last start. He just made some mistakes."
Minnesota's offense, meanwhile, was mostly held in check by Yankees right-hander David Phelps, who allowed a fourth-inning Morneau homer before running into trouble in the seventh.
The Twins scored three runs in the seventh, with Pedro Florimon and Dozier providing back-to-back RBI singles before Joe Mauer plated Florimon with a sacrifice fly to left field. Morneau capped the scoring with a solo shot off Boone Logan in the eighth.
But it wasn't enough for the Twins, who were outscored, 29-14, over the four games of the series.
"Offensively, we didn't do an awful lot," Gardenhire said. "We kept battling through it. We made some better swings as we went along. We were within striking distance, but then they finished us off at the end. So it was a disappointing homestand, losing the last game to the Royals and then having the Yankees come in here and take it to us and outplay us the whole series."