Call vue method from Mapbox popup

I have a mapbox popup, and inside the popup I would like a button to call a method defined inside my vue component.

My popup:

const popup = new mapboxgl.Popup({ focusAfterOpen: false })
        .setLngLat(coordinates)
        .setHTML('<button id="button" @click="myMethod">Click here!</button>')
        .addTo(map);

My method:

myMethod() {
  console.log("clicked");
},

I was able to add an event listener to the button, which is working. But I don't get a function execute which is defined inside my Vue comonent.

My Event Listener:

var button = document.getElementById("button");
      button.addEventListener("click", function() {
        console.log("clicked");
      });