An air carrier pilot reported they received a reroute via CPDLC. They failed to read the whole message and loaded the route incorrectly causing them to deviate off course.

Narrative

ATC issued a revised clearance via CPDLC. Clearance was - load new route to LEV. Rest of route unchanged. Free text stated GLADZ.LEV.../IAH. I did not notice the route portion of the message because it was so short; and thought the clearance was only to proceed direct to ZZZ. First Officer (FO) did not notice the error either and programmed the FMC for direct LEV with abeams as I directed; without GLADZ. ATC noticed we had turned to LEV and not GLADZ; and asked if we were proceeding direct to LEV. He stated that he must not have sent the message correctly and then verbally cleared us Direct to LEV. I believe he was trying to be kind and let us off the hook. In seeing the CPDLC message 'load new route to LEV' I simply assumed it was to go just direct LEV and failed to read all of the message and use the LOAD prompt to load the FMC from the CPDLC clearance. I wanted to manually program the FMC with the Direct in order to utilize the abeam waypoints function. Expectation Bias.In the future I will be certain to read ALL of the incoming CPDLC message; ask for confirmation from other pilot and to use the Load new ROUTE function and then reverify the clearance from the CPDLC against the FMC before executing the new route in the FMC; using the pilot monitoring (PM) to verify the new clearance loaded correct.