Applying to a PhD with a weak masters thesis
First, you may be judging your own work more harshly than is warranted. It may not be as weak as you think. It is fairly common for problem to appear easier after it is solved than before you began. 

Second, no one is likely to read your master's thesis as part of a doctoral application. They will take note of it, and any grade you got, and the general field. At most a few people will read the abstract. They are too busy to read it, frankly. 

Third, an application for doctoral study is normally judged on a wide range of criteria with different candidates scoring higher or lower on the various elements. But the overall picture is what is important. "Does this candidate have the necessary background?" "Does this candidate have a good chance of success now and hereafter?" And since most programs are competitive, "How does this candidate compare with others in the pool?". 

But, if you are accepted then you still have two hurdles. The first is passing comprehensive qualifying exams. Some advanced coursework may still be needed to get you to that point. The other is writing an acceptable thesis under the direction of an advisor, along with whatever research enables that. 

In the US a lot of doctoral students enter the program with no research experience at all. You already have an advantage there, no matter how your recent thesis turned out. And, even at the doctoral level, not every dissertation has the same impact. It represents early work, not the person's best career work. 

Make sure your CV is solid with your background accomplishments. Don't negatively characterize your thesis. Make sure your SoP explains your goals, short and long term, along with how your background supports that. 

And, though you name a specific school, don't cast a narrow net for a doctoral program. Give yourself more than one chance.