My inventory count was different than yours. I had 369 pieces but slightly different composition. I had 85 British, 97 US, 72 Russian, and 91 German units. The specific units were also slightly different.
I too had a slightly different parts list- I had one fewer British infantry and one extra German artillery piece. I suspect that every game might have slightly different numbers for the units.
Go to MB/Avalon Hill website and look up the games. In their support section, they will describe the process by which you can check to see if you have a game that received and insufficient amount of game pieces. Contact their customer service and they will send additional pieces.
I received my games well over a year ago and just recently opened them. They sent me replacements with no problem. I believe they shorted German infantry and another unit that I can't recall.