I think the answer is definitely yes, it looks like you'd have to do the same thing as I've just done to my electric folding bike, change the crankset and chain.
The Sakura has a standard cotterless bottom bracket and crankset, but uses a small (around 40 tooth) front chain ring. You can't fit a smaller rear top gear sprocket, as it uses a 6 speed free-wheel, rather than a cassette, and these only come in a very limited range of tooth sizes, 14-28 is most probably what you've got and you'll struggle to find even a 13-28, let alone anything taller. There's also an issue with the rear dérailleur, as it probably won't handle anything smaller than a 14 tooth top rear sprocket which is almost certainly what you have at the moment.
You can't just change the chain ring, unfortunately, as it's not bolt-on type. You can change the crankset for one with a 50 tooth chain ring (about as big as you can get in single speed 3/32" chain rings) though and this will make a significant difference. You will also need a longer chain by around ten links.
I bought a Stronglight 50t 170mm crankset for £28 from this ebay seller: http://stores.ebay.co.uk/derekscyclesonline
and it seems pretty good. A new 3/32" chain cost another £7 from the local bike shop. It was a ten minute job to swap the cranks over and fit the new chain, but you do need a crank puller tool to get the cranks off the bottom bracket axle. These are only around £5 or £6 , but you could ask if your local bike shop would let you borrow one if you're only going to do this job once.
I think you will find that a big front chain ring will transform the pedalling ability of the bike at speed and allow you to use all the gears sensibly. If your bike is anything like mine, most of the lower gears were pretty useless as they stood, I rode in top gear 99% of the time and even then struggled to pedal fast enough on the flat.