You can have Phaser listen for keyboard events on the game canvas only (not the browser window).
<canvas autofocus id="canvas" tabindex="0"></canvas>
new Phaser.Game({
autoFocus: false,
canvas: canvas,
type: Phaser.WEBGL,
input: {
keyboard: { target: canvas },
mouse: { preventDefaultDown: false }
}
// etc.
});