Playing in front of their home crowd, the Hammers needed a 96th-minute free-kick from star midfielder Dimitri Payet to win the tie 1-0 on a night where Bilic expected a much simpler outcome.
"The main thing was to go through," said Hammers boss Bilic. "We expected an easier win, with the greatest respect, and not to have to do it in the last minute.
"We went down to 10 men but we wanted to score before extra time and then, a great moment from a great player. We didn't play good but I thought we deserved to win.
"It was not exactly what we wanted tonight - but it's a win."