if you want to use a coaxial feed, you cannot really design a matching network, so you have change the location of the feed point. Another method is adjusting the width of the antenna. This should not change the resonance frequency by a lot but it will change the impedance of the patch. If these dont work, you can try making some cuts in your patch.
-12 dB is good enough for most applications anyway, as long as you have a good bandwidth. Anything below -9 or -10 db is ok. It is a dB scale so your losses at -13 dB are 5 percent and at 20 dB they are 1 percent. So one would rather have a better bandwidth than a low S11. The losses will be much higher than 1 percent in practice in any case.