Daniel Farke’s men won promotion to the English top flight last summer but they have won just five league games all season and their defeat to the Hammers was their 24th of the season from 35 games.
Michail Antonio was a thorn in their flesh throughout the game, and the Englishman finished the day with four goals –two in each half– before he was substituted in the 78th minute for Sebastien Haller.
West Ham’s victory has taken them into 16th position, six points clear of the drop, to ease their own relegation fears with three games to go.
Speaking to BBC Sport, Norwich manager Farke could not hide his disappointment as Norwich became the first club to be relegated from the Premier League on five separate occasions.
"We are unbelievably disappointed," the German manager said.
"When I came here we needed to develop young players and sell them to keep the club going. We were able to do this. Then the second season no-one expected anything but we were able to stage a miracle that no-one expected. We won the Championship title with a special brand of football. We were not able to add a third miracle in a row against all odds.
"I’m really disappointed for this and for all our supporters. We wanted to beat the odds again but when the dust settles the outcome is more or less what was expected. Our teamsheet had more or less the same players as last season, with some key players out. It doesn’t take anything away from the fact that we are disappointed.
"From the first day after promotion our chances to survive were perhaps 5% so in 19 out of 20 cases you will go down. If you have luck and no injuries, then you have a chance. When we are 100% we are competitive but when it’s 96 or 97% then it sometimes looks like men against boys. That’s what I expected.
