Airport to Shimbashi

I plan on buying a Narita exp 1500yen ticket from airport to the city. I need to get to Shimbashi, but the train does not stop there. The express gets into Tokyo station track 1, and a local Jr train pulls out of track 1 a few minutes later. Do I need to exit the track area and buy another ticket for this last 3 minute ride. I'm not planning to activate my Jr pass for another week, when I leave for Osaka.