Slaven Bilic not pointing fingers after Sunderland draw
Andre Ayew fired West Ham ahead with just five minutes gone only for Wahbi Khazri to level direct from a 26th-minute corner.
James Collins headed the Hammers back in front within two minutes of the restart, but Sunderland substitute Fabio Borini struck in the 90th minute after an error by Randolph.
However, Bilic has refused to criticise his goalkeeper.
Darren Randolph had a shocker against Sunderland
"There is no pointing fingers," the Hammer manager said. "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.
West Ham dropped two points against Sunderland Premier League table based on 2017 results Sat, April 15, 2017
How would the Premier League table look if just results from 2017 counted?
Play slideshow Getty Images 1 of 20
20. Sunderland (6 points from 12 games) W:1 D:3 L:8 G/D -14
"To concede both goals in this way, they were both strange goals and of course you are not happy with the way we conceded.
Get Quotes on Home Insurance
"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."