Joyce, still a huge fans' favourite with the Tigers, was the top target for the managerial post at the KC Stadium when Nigel Pearson departed for Leicester last month.
However, the 46-year-old opted to stay at Old Trafford to continue his fine work with the club's second string, with his team ending the year at the top of the Barclays Premier Reserve League North.
"We're delighted [he's staying] because there was obviously a concern when he was offered the Hull City job," Sir Alex told the latest edition of Inside United.
"The thing about anybody working here is that they know their job is safe, whereas if you join the managerial merry-go-round, you’re in trouble if you lose three games.
"But he does a great and very important job with the Reserves, and he’s helping [Paul] Scholes settle into his new role, and Scholesy is enjoying working with Warren because he’s a really good professional."