Almost every product out there designed to cover that ugly concrete floor requires a gap for expansion and contraction. Sure there are a lot of great, cheap ways to deal with those gaps.
One of our favorite products for this is the Diamond life base molding. While it can be slightly expensive, it provides an amazing look and ties the floor and the wall together. There are plenty of additional options available as well. Many customers will use a roll of rubber cove base or even a wood base molding.
Whatever product you decide to use just make sure you tack it in such a way that it is barley touching the floor. You should be able to slide a dollar bill between the floor and the molding without issue