Why wouldn't other receptacles work after I changed a receptacle?
Most likely the outlet was part of a chain of outlets - so there would be at least 2 cables of 3 wires each (hot, neutral and ground).

All of the hots need to be connected together and to the outlet.  Same for the neutral and ground. Often this is done by using the screws on the outlet itself - connecting BOTH hot wires to the two screws for hot.  Only connect one wire per screw.

If you connected it exactly the same way as it was before it should work.  Did you break off the little tabs between the sets of screws?  Were they broken off on the old one?  Make sure they are the same.