Inducer Fan Blowing Out Flames and Pilot Light on Carrier Furnace?
It would be very, very odd for an inducer motor to blow out the burners and pilot.  If it was the case, and since inducers come on before the burners are ignited, I'd expect it to blow out the pilot before the burners ever ignited.  That pilot is much easier to blow out than the burners.

My suspicion is this: Furnaces that use inducer motors often have pressure sensors that detect whether or not the furnace draft is properly in place.  If it is not, the gas to the burners is shut down (I wouldn't be surprised that the pilot is shut down, too, for safety purposes &mdash; nowadays most furnaces with inducer motors use electric ignition to avoid the issue).  This is actually a good thing.  An improper draft can cause big trouble in your house (like everybody-dying-from-carbon-monoxide-poisoning trouble).  So this is a behavior you want to have.

Many furnaces have an LED light that blinks an error code when this occurs (my light in in the main blower area, not the burner area, but there is a small transparent window so I can see it... in the dark... with my hands over the window...).

Something getting in the way of a proper draft is more likely your problem.  It could be caused by the new motor not having enough umph for the exhaust setup in your house or a pressure switch having become too sensitive over time.  It could also be caused by dirt/dust/spider-webs/buildup in your exhaust pipes or something partially obstructing the exit (most are on the roof, but if yours in on a side wall, are there plants grown up around it?)

What's important is to find that LED (I'm hoping you have one) and either getting out your furnace's manual or finding it online and checking out what the error code is.  The blink code would happen right after the burners are shut down.