ls *{369..422}*.avi >/dev/null
This will first generate patterns like
*369*.avi
*370*.avi
*371*.avi
*372*.avi
*373*.avi
*374*.avi
through the brace expansion, and then ls will be executed with these patterns, which will give you an error message for each pattern that can't be expanded to a name in the current directory.
Alternatively, if you have no files that contain * in their name:
for name in *{369..422}*.avi; do
case "$name" in
'*'*) printf '"%s" not matched\n' "$name" ;;
esac
done
This relies on the fact that the pattern remains unexpanded if it did not match a name in the current directory. This gives you a way of possibly doing something useful for the missing files, without resorting to parsing the error messages of ls.