The Hammers blew a 2-0 halftime lead, with Chelsea's winner coming in injury-time.
Nuno said afterwards: "I’m disappointed, sad, frustrated.
"It was a game we started really well. We were really good in the first half. When you score two goals away from home, it should be your game.
"In the first half we combined and we defended well. We were in control and every time we went forward, we combined and we scored two beautiful goals.
"That's a frustration, not being able to sustain our performance through the game. We knew that Chelsea were going to react.
"We should have done much better to defend our own box. We should have done much better. We allowed their centre-back to step in and cross and after that we tried to survive and couldn’t.
"It was the moment that we felt when Chelsea scored the first goal (that we went to a back five), that the wide areas were not in (our) control, our wingers were not able to control their full-backs to allow Malick (Diouf) and Aaron (Wan-Bissaka) to go stronger.
"At the same time, we have to defend the box. When they cross, we have to defend it, and we didn't."