The relegation is estimated by club sources to cost West Ham £200m in lost revenue, following a reported loss of over £100m in their latest financial accounts.
"While the ultimate outcome on Sunday was a painful one, the board of directors believe that there have been broader signs of improvement and progress in recent months, and we want Nuno to continue developing that progress," the club said.
The hierarchy pointed to statistical improvements under Nuno, who took over in September after Graham Potter was dismissed, as a key reason for their confidence.
"A total of 25 points taken from our final 17 Premier League matches equated to 1.47 points per game – a ratio that would have resulted in a 7th place finish across the total season.
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Furthermore, we feel the clear improvement in squad mentality and togetherness since January, leading to that upturn in performances and results, makes him the right man to lead us forward," the club said.
Financial strains mean the club will likely sell key players, with skipper Jarrod Bowen and midfielder Mateus Fernandes attracting interest, while Roma is targeting winger Crysencio Summerville, according to La Gazzetta dello Sport.
"For every single person who is passionate about the club, it (relegation) hurts deeply and that feeling will sustain for some time," said West Ham.
The club also addressed fan frustration regarding the 2016 move to the London Stadium and the recent departure of vice-chair Karren Brady due to supporter abuse.
