Don't beat yourself up. In a few months you will be a pro. Depending on the seat and your car it can be tough. You should be able to move it side to side no more than an inch. Go to a fire station and find a certified tech. My husband and i are pretty good at seats I think and even we couldn't get this one convertable to install tight in my car, but sure enough it fits well in my mils car.
i'm sure it will be fine - have you googled for any videos of your seat being installed in your car? we checked youtube for some videos before deciding on a seat to be sure it would fit in our smaller car. i'd check out some videos then give it another go.
ETA: "it will be fine" like it's completely fixable/able to be tightened, not that a loose seat is fine.
Also you only check for movement near the seatbelt not at the end of the base that hangs off the front of the seat. Just check for movement with one hands and give a little shake side to side...you're looking for less than one inch of movement side to side.