Magic takes energy from its surroundings in order to work.
Think of it. If you use magic to levitate a rock from the ground to the top of a table, you just put some potential energy in that rock. The energy was provided by magical means, so the magic needs to take that many joules/calories from somewhere else.
In the absence of viable energy sources for machines, that energy may be the very calories stored in the body of the mage. But this would disable or kill a mage who tried to do something big on her own. Magic may draw from the same energy sources that machines use so that the mage can accomplish greater feats. For example, if you have gasoline or coal nearby, magic may take energy from the chemical bondings in those.
Explanation: when you burn wood, coal, gas etc. for fuel, you are extracting the energy in their chemical bondings. If magic has already drained that energy, then those sources of fuel become useless for engines, for example.
As a side effect, magic may either be literally burning those to fuel itself, or it may extract that energy through means other than combustion (after all, magic is a magical thing), chemically turning coal, wood, gas etc. into other substances.
If there are electrical currents running in metal, magic may take energy from there. This starves electrical machines off of energy.
And so on...
The cool thing about this method to explain how magic interferes with technology is that it does not cause magic to simply cancel out tech... It makes both compete for energy. So it takes a lot of magic to stop a huge machine, for example, or a large concentration of tech to starve off a really powerful spell.
This also allows you to do some back-of-napkin calculations as to what you could achieve given some source of energy. For example, with access to a 220V socket, you could heat food just like a microwave oven would (but without the need for that oven), or you could set small things on fire. But if you sap the tank of a car that is full, you can move a ton of stuff for a few hundred miles. Or you can fly yourself for ten times as much distance. Or you can cause a projectile to fly at hypersonic speeds! Be creative ;)