Martinez got anxious.  A 2-2 pitch, 2 outs, he was going for the strikeout to end the 1st inning.  Nothing wrong with that.  It all came down to how well he executed his mechanics to locate the Slider. Martinez clearly wanted to throw the HECK out of the Slider and slay the biggest power threat in the game.  

When this happens, the pitcher rushes his rhythm and tries to throw the Slider in the arm swing out of the glove.  What results from this flaw?  The hips fly open too soon, the front shoulder opens to soon, and the arm and hand fall underneath the baseball, instead of staying behind the ball.  This forces you to release the Slider too soon.  

When the hand is not behind the baseball, it is impossible to throw the Slider with the downhill tilt that makes the Slider downright nasty.  Also, when the hips and shoulder fly open too soon, the hitter gets a good look at the release of the baseball, thus being able to visually pick up the ball sooner.  

...It goes without saying, the 'Hanging Slider' is Disastrous....although very preventable

The point of contact that Giancarlo made was at the mid thigh,
over the plate.  This is a Nitro Zone for hanging Sliders.
Think Down Hill with the Slider.

Its a Simple Matter of Patience and Trust

PATIENCE - Not get too amped to throw the pitch.  Keeping a good rhythm in his is delivery.

UPPER HALF - Not rushing the arm swing out of the glove.  Focus on getting on top.  

LOWER HALF - Lead with his front hip towards his target. Stay sideways in his stride a split second longer, rotating the hips later.  This later rotation will allow him to get out in front with the release of the Slider, throwing it downhill.  

TRUST - Trust in your mechanics that if you do everything right, the Slider will go where you want it to go.  There is no reason to feel the need to improvise on the spot or let emotions overtake your muscle memory.  

It doesn't matter if you are facing the 4 hitter or the 9 hitter.  You want to keep your mechanics as simple as possible.

Carlos Martinez does fall of to the 1B side of the mound on his release of all his pitches. However, it’s still a matter of staying closed with his front hip just a split second longer.  If he was able to execute this simple adjustment, he would more likely have buried the Slider down and away where he wanted it located.
Sending Big G back to the dugout, forcing him to make an adjustment.

Maintaining a comfortable rhythm in your delivery and consistent execution of your mechanics will give you the best opportunity to succeed on the mound.  The Hanging Slider is a part of the game, however, these simple adjustments can severely reduce it's ugly presence when you are pitching.

Now the Cardinals did come back to get the win the game, 4-3. For Martinez, it was his 8th Win of the year, as he went 7 IP with 9Ks (Freezing Giancarlo his next time up on a 95 MPH 2 seamer on the outer half).  

All competitive pitchers want to get mistake pitches back,even in Victory.  It’s what drives pitchers to keep getting better and making their mark on the game.