Rather than count phrases,( because sometimes you just do not have the time or cannot count that fast) learn to recognise the groupings. Every time you come across a grouping of notes learn how the grouping or phrase plays rather than sounds, then look for others with the same grouping and phrasing and you will see that in the case of this song that this will repeat regulary in the piece.
Because this is a common "feel" you will then recognise it in other songs and music you see. If you now apply this idea to other beats, grouping and phrasing you will build up a dictionary or rhythms and beats, which like words you will recognise when you see them and immeadiatly know how they play rather than how the sound. So in effect you are treating phrases and grouping as words with a meaning in rhythm, and looking for these "words to repeat in the music"
How they sound will depend on the pitches of the notes used, but the rhythm will always be the same. I would say practice these points on a single line or space on the staff so the pitch of any notes does not detract you from the rhythmic quality you seek. By seeing the rhythm of these "words" you are now free to work on the actual playing of the notes in there correct pitches and fingerings without also having to worry about how they feel...you have infact internalized these rhythms