Slaven Bilic described Wahbi Khazri's stunning goal direct from a corner as 'strange' but refused to criticise his players.
The Hammers took the lead with just five minutes on the clock through Andre Ayew before Khazri - in from the cold after almost six months without a start - scored an equaliser direct from a corner.
The corner managed to evade both Sunderland's attackers and the West Ham defence to sail straight into the net on an eventful afternoon on Wearside.
Defender James Collins headed the Hammers back in front within two minutes of the restart, but substitute Fabio Borini, who had been on the pitch just minutes after replacing defender Billy Jones when he was carried from the field on a stretcher with concussion, struck in the 90th minute after an error by keeper Darren Randolph.
Bilic, who also saw full-back Sam Byram dismissed for a second bookable offence during 10 minutes of stoppage time, refused to criticise Randolph after he mishandled a deep Darron Gibson ball into the area, with Borini taking full advantage.
Bilic said: "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.
"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."
In particular, Bilic absolved Randolph of blame for Khazri's freak strike.
He said: "If we are talking about the goalkeeper for that 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."