Yes, it is due to you importing from Gmail. There should be a contact group in Contacts for the Google contacts. And those contacts will not sync with iCloud (separate services).
If you have a PC or Mac, can sign into Google, export your contacts as a vCard file, then import that file into iCloud.com (Contacts > Gear/Settings/lower-left > Import vCard). Then can select and drag those contacts to iCloud group(s).
Can do same on Mac via the Contacts app.
ADD: There are some apps in the App Store that will do the syncing for you.