Digital upgrades can be really elusive to hear right off the bat, especially if you've never listened for them before, but often even if you have. In many cases the differences only fully manifest themselves over extended listening. In my system, many digital upgrades later, there are still certain disks where, if I level-match the sound, I can have a heck of a time trying to pinpoint meaningful improvements between the sonics of my reference front-end separates and that of my CD-R recorder/player. There are other times, though, when it's much more obvious, and of course recording quality can have a lot to do with this. Your CDP must at least be pretty decent however, because some of the easiest-to-hear digital differences I've encountered have been among various low-budget players, and if yours was a mediocre one, I'm sure you wouldn't have felt the need to post this thread.
I would say you should give the new DAC some time, if you can, whether for component break-in or just for your ears to acclimate and begin to pick up on subtle stuff (reduced transient smear, better articulated microdynamics, juicier timbres, clearer air around the players, more pitch-defined bass...keep on listening). All digital converters, just like all other gear, will exhibit *some* sonic differences amongst themselves, whether for better or for worse - it's not really possible that your new DAC and your old CDP would sound *exactly* the same. But having said that, I'll also add that the quality of both the transport and digital IC can have a pronounced limiting effect on the theoretical improvements offered by a better DAC, and I was never able to get the kind of improvement I was after until I stopped using my old players as transports and got a real dedicated one.
On the other hand, what's perceptable and what's meaningful can be two very different things, both system- and listener-dependent. If you're happy with the sound of your inexpensive CDP, and don't suspect that the incremental improvement you might realize in your system by further pursuing the separates issue would be worth the expense to you in terms of musical enjoyment, then consider yourself lucky and save your money for recordings instead.