Hey Jaila,
I am not an expert on varying tone or accents in another language. However from what I have heard from others who have learnt Japanese and speak it at a almost native level (those who live in Japan or who have learned it outside of Japan), it seems as though it is natural to sound different when you speak Japanese than when you speak English.
I don't think there is a way to change that, since in order to speak a foreign language you have to mimic native sounds which could cause your tone to either be more upbeat or serius than your usual tone. I don't think it something to be worried about.
Hope this helps ;)