Thanks for the comments.
I am shooting with Aperture priority and using a telephoto lens shooting at 210mm focal length with aperture of F/5.6.
The trick of creating a blur background with the above settings is you need to have the camera positioned close to the water or ground in this case so that the actual background is far away from the subject. And that is why I was using a liveview to take that photo. I could not lay down on the ground at that time because I shoot that photos during lunch break and was wearing with shirt and tie.
If you stand up and take the picture or not trying to position the camera to the same level to the subject, the background is going to be very close to the subject. As a result, you cannot create a blur background.
And I was focus on the eye.