If you did a system-wide installation of tcl, you most likely forgot to run ldconfig (and possibly add the location of the libs to /etc/ld.so.conf).
If you installed it in your home directory, you'll either have to set the LD_LIBRARY_PATH environment variable prior make install and everytime you start your eggdrop; recompile your eggdrop static; or relink it with an --rpath directive stating the location of your libtcl8.4.so.