The head coach was direct in his assessment of a performance he described as poor from the first minute, with two defensive errors inside the opening 20 minutes ending any realistic chance of a result at St James' Park.
"Of course it hurts, it hurts deeply. It's tough. We started the game really badly. The way we conceded and the spaces that we gave to Newcastle players made our task really, really hard. It was a bad performance."
Woltemade's 15th-minute opener came from a Harvey Barnes cross after goalkeeper Mads Hermansen's miscontrol allowed Newcastle United to retrieve possession. The second, scored by Osula four minutes later, came from slick combination play involving Kieran Trippier, Bruno Guimarães and Jacob Ramsey before the Dane finished cleanly. The third, Osula's second, came from a defensive lapse at a throw-in in the 65th minute.
Nuno made changes in an attempt to alter the pattern of the game, withdrawing Jean-Clair Todibo early to introduce Castellanos and switching from a back three to a back four. The moves produced more attacking threat but could not repair the early damage.
The West Ham manager acknowledged the fans' frustration was fully justified.
"I apologise to our fans. They showed their frustration and with reason when they see a team that doesn't make them proud. It's right, it's right, and today we didn't make ourselves or them proud. Our final match of the season is going to be at London Stadium and we owe it to our fans to show a better performance."
Nuno confirmed there was no prospect of giving up on survival.
"We're going to work hard, see what can happen on Tuesday at Chelsea. If it's possible, we'll give it a go, but realising that it's really hard."
West Ham United were relegated in 2011 before bouncing back immediately. A second relegation under the current ownership would represent a significant step backward for a club that reached two European finals as recently as 2023.