Lingard, who enjoyed a successful loan spell at West Ham during the 2020-21 season, signed for Forest last month following the expiry of his contract at boyhood club Manchester United.
"I was surprised, yeah. I thought Jesse in the end would come here and I've got to say the club made him a really good offer," Moyes told reporters ahead of their Premier League opener at home to champions Manchester City on Sunday.
"You couldn't turn around and say David Sullivan and the owners didn't do everything they could to get him. They certainly did."
West Ham brought in Nayef Aguerd (26), Flynn Downes (23), Alphonse Areola (29), Gianluca Scamacca (23) and Maxwel Cornet (25) during the close season but Moyes admitted that the transfer market had been difficult to navigate.
"We've made bids for numerous, numerous bids. Genuine bids and genuine money and different reasons we've not got them. They've not wanted to come to the club or we've not got the financial deal right," he said.
West Ham finished seventh last season, securing a place in the Europa Conference League.
