The Ghana international was at hand to head home a rebound as the Hammers recorded a 2-1 away victory in their last league game of the season.
Sam Vokes put the home side in front after 23 minutes while Sofiane Feghouli snatched the equalizer for West Ham, with Ayew eventually sealing victory for the visitors.
“The second goal may have benefitted from a touch of luck, but the whole action was for me brilliant,” Bilic said, according to his club's official website.
“How it finished, OK, it was a bit lucky, but we came with a lot of players there [in the box] and that’s why that rebound fell to Ayew, like it did for Lanzini’s goal against Spurs.
“You have more chances that the ball will drop to your player when you have five in the box.
“Andre Ayew is great at being in the right place at the right time. We came there, so alright it had an element of luck but we deserved it.”
Having joined West Ham on a club record £20.5 million deal in August last year, Ayew finished the season with six league goals.
His early days at the London Stadium were far from his expectations as a hamstring injury on his debut forced him out of action for almost three months.
However, after finding his feet, Ayew hit five goals in the second half of the season to help Bilic's outfit finish 11th on the log.