This is a common problem which I hear often.  “I just started feeding birds, and now I have Grackles and other large birds eating all of the songbird food.”  There are solutions to this problem.  Usually, the solution involves purchasing a new feeder.  You can also try changing bird seed.  Songbirds love thistle seed, either a thistle sock or a thistle feeder.  You can also select one of the thistle seed feeders available at Barn in the Sticks, which has an feeding port below the perch.  This allows more agile birds, like goldfinch to feed, but sparrows and other nuisance birds will leave it alone. 

Another alternative are feeders available which have a mechanism on them, which triggers on the birds weight.  They also work for squirrels and other animals trying to get at your feeder.  There is a line of feeders from Droll Yankees, which have spring loaded perches which drop, battery operated perches which spin, based on the weight of whatever is sitting on the perch.(pictured below, the Droll Yankee Flipper, when a large bird or squirrel hops onto the feeding perch, the perch spins, knocking the large bird or squirrel to the ground..or to flight)

There are also feeders which if the weight is too much on the feeder; the feeder port closes, so the bird or animal cannot get to the seed. 

All of these feeders come in different sizes and prices, so it possible to fit into your budget and décor in your yard.