The reason the "Check Engine" light, called the Malfunction Indicator Lamp (MIL), exists in cars is due to legislation. Road vehicles have strict EPA standards to follow regarding emissions that include not only the exhaust and air/fuel mixture, but the fuel tank evaporation, and crankcase oil ventilation. The only way to meet these standards is by computer control of the engine and other aspects of the vehicle. The light is mandated to indicate when any one of these systems isn't operating within specification, and thus may have higher emissions than what meets the standards.
While drivers think of the light as an early warning indicator for vehicle trouble, the reality is that its primary purpose is to encourage drivers to keep their vehicle within the emissions standards it was originally designed for. These change over the years, newer cars have more strict standards to follow.
Small aircraft follow the non-road emissions standards, similar to construction equipment, lawnmowers, generators, and off-road vehicles. None of these are required to follow such strict standards (though they must meet minimum standards, and these are getting more involved), and the standards they do follow can be done with no computer control. There is no legislation that requires a lamp indicating that the engine is operating at higher emissions than intended.
Larger aircraft have lower emissions because they are required by customers to be very fuel efficient, and one way to increase fuel efficiency is to add computer control that uses as much energy from the fuel as possible, thus burning it more completely. These systems are expensive, though, and only make financial sense if the aircraft is going to be flown many, many hours over its lifetime. They also do follow stricter standards, but the indicator lamps and manufacturer diagnostic equipment are more comprehensive for these aircraft to enable overall cost-savings and increased reliability/safety required for passenger service.
The EPA is due to make recommendations in late 2015 and early 2016 that will affect aircraft emissions. At that point in time it may be that new aircraft will need to be under computer control and will need a check engine lamp.
This might be fundamentally different though. In a road vehicle if there's a problem, you don't need to know what it is to be safe - you can pull over and call a tow truck. Aircraft have no such luxury, so while there may be a lamp indicating excessive emissions, chances are good pilots will still rely on multiple other indicators to determine what malfunction has occurred so they can respond best to the circumstances.