A controversial 90th-minute penalty from Charlie Austin was enough to earn all three points for the Baggies - with that result seeing them return to the top of the Championship.
The spot-kick was awarded after keeper Declan Rudd was judged to have brought down Kyle Edwards - with the home fans adamant the winger had dived.
Bilic, speaking post-match, insisted he had not had a chance to properly review in the incident.
But over the course of the 90 minutes, the head coach felt Albion had been the better side.
"It’s a big result," Bilic said.
"They knew we were coming. We are doing well at home, but we are nowhere near them - they have the best record.
"But straight away from the start, it was us. In the first half we were very dominant, just what was lacking was the quality in the final third.
"I didn’t expect it to be that one-sided in the first half.
"I told the guys to be patient, to raise the tempo, come on, come on, come on.
"In the second half they (Preston) improved. I wouldn’t say they were the better team, but they were better. They had their moments.
"Then we made some changes and the last 20 minutes it was a game. Not all us, but pretty much all us.
"To be fair we were pushing but the clock was ticking.
"You’re thinking ‘okay’, a point is good here. Just don’t concede a goal. Then we scored.
"What I’m trying to say is that we definitely didn’t deserve to lose, if anyone deserved to win it was us.
"When it has come so late in the game, without us missing so many chances, then a point for them would’ve been also okay."
On the penalty incident, Bilic said: "I didn’t see the replay. I saw it on an iPhone and to be fair I didn’t see it properly, only from behind.
"Funny thing was that one of their bench said it was a penalty, somebody from our club said he wasn’t sure.
"It should’ve been the other way around. There are going to be some sackings in a couple of days!"