I've always done mine using the wrenches in the bike's tool kit, and so far no problem. Ideally you should check the chain's tension with a rider on the bike, to ge an accurate measure.

The chain will stretch over time, and the more aggresively you accelerate, the more often you'll have to adjust it. It's a good idea to check chain tension at least every time you lube the chain. Checking before each ride is even better.