The quick answer to your question: the part you've replaced probably goes on the other side. Try fiddling with the brackets and see if you can get it to work. I remember of the 3 times I've put the engine in, 2 times it went in smooth like butter and took some blood, sweat and profanities before it fit.
A couple of follow-up questions so that I can understand your issue better and give you better answers:
What part of the motor mount did you replace? In the original setup, there were 3 pieces. There was a metal bracket which bolted onto the frame and provided a small platform with a bolt hole in the middle, a metal bracket that bolts onto the block and has a fat block of rubber with a bolt sticking out at a 135 degree angle, and a much smaller angled bracket that bolts onto the rubber bit, and goes through the hole on the frame brackets.
As I recall, when I finally got things situated, it was a matter of getting the metal/rubber bracket that bolted onto the engine and the smaller angled bracket in the right combination. If memory serves me, both pieces are keyed and provide different positioning results when reversed.
Pictures would be a huge insight

Hope I was able to answer your question!