This is expected behavior since the new domain has not started to rank on Google. You will need to setup some redirections from the old domain to the new one to be sure that you do not hurt your SEO.
To achieve this, you will need to maintain the old domain as long as you can and also add the following redirect on the old site’s .htaccess file:
RewriteRule ^(.*)$ http://www.newdomain.com/$1 [R=301,L]
This will in effect redirect all the users that click on the old URLs on the SERP to the new domain.