The Black Cats twice came from behind to rescue a point at the Stadium of Light, with Wahbi Khazri scoring directly from a corner before Randolph spilled the ball at the feet of Fabio Borini for a stoppage-time equaliser.
Bilic admitted that he was unhappy with the manner of both goals, but insists that Randolph is not solely to blame.
"There is no pointing fingers. We are a team. We are playing as a team, we are winning as a team, we are drawing as a team, we are losing as a team and we are conceding goals as a team. That's it," he told reporters.
"Of course you are disappointed when you are leading twice and then you concede this late - although it was 10 minutes of added time, which is a long, long time, but I have to say it's a fair result. To concede both goals in this way, they were both strange goals and of course you are not happy with the way we conceded.
"If we are talking about the goalkeeper for [Khazri's] goal, it's very hard for a goalkeeper. The ball was not very high in the air so he could [not] have seen it all the way along. Everybody was expecting our player to clear it, but he didn't and the ball dropped very quickly and he couldn't get a touch. It's a very unusual goal we conceded."
West Ham moved up a place to 13th in the Premier League table with the point, although they have now won just one of their last nine outings.