Those who say, 'My vote doesn't even count', are just using an excuse why not to vote, not a reason why they don't vote.
Let's put it this way. (I'm sorry, I work in examples.) Let's say there is a village of 100 people living on a beach at the bottom of a cliff. All they can eat are coconuts that grow on trees at the top of the cliff. The cliff is not too steep, anyone in the village could climb it, but it is an hour climb. 40 people in the village regularly make trips to the top of the cliff to gather fresh coconuts to eat and the remaining 60 eat the old coconuts that fall over the cliff.
If you ask those 60 why they don't climb the cliff, they might say "Why? I'm eating coconuts anyway?" What they don't want to say, but is the truth, is "I get my coconuts, and it's not worth an hour trip just to get better coconuts."
Voter apathy has more to do with their contentment at getting the scraps that roll down to them than philisophical disillusionment with the results.