The IP inspect uses CBAC which works the same way as SPI function on a regular firewall. There are 3 steps.
1. configure NAT/PAT (which you have done)
2. Allow the required traffic outbound (ACL)
3. Create the IP inspect rules and apply them to the interface. The IP inspect rules should contain the traffic that should be permitted back in (replies to outbound requests) even though the ACL denies
** Creating INSPECT ***
ip inspect name MYTRAFFIC ftp
ip inspect name MYTRAFFIC http
ip inspect name MYTRAFFIC https
** Applying to interface **
On the interface you wish to permit the traffic
ip inspect MYTRAFFIC out