Watford defender Craig Cathcart diverted Wes Hoolahan's cross into his own net before halftime before Odion Ighalo lashed home Deeney's cross shortly after the interval to give the visitors hope.
That was quickly snuffed out, however, when Mbokani grabbed his second goal and Norwich had chances to extend their lead before their relegation was confirmed after one season back in the top flight.
"It is severe disappointment," Norwich manager Alex Neil said.
"In recent matches we have known it was going to be a difficult match. We had it in our hands five matches ago but we came up short," he added.
"The story for us is that as a club, we have dropped short for a variety of reasons. We have made vital errors in games at crucial times and the recruitment has not been as good to strengthen the squad."
Neil described the club's supporters as "humbling".
"We have not given them too much to shout about and that makes it harder for me to accept for letting them down," he said.
"I am here to do a job, the club will be bigger than me and I am not fearing for my job."
(Writing by Ed Osmond; editing by Clare Fallon/Toby Davis)
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