The Hammers were left frustrated in their pursuit of several targets, with Leeds United stars Kalvin Phillips and Raphinha and Benfica striker Darwin Nunez believed to be high on their list of priorities.
Speaking to the press ahead of Saturday lunchtime's FA Cup clash with non-league side Kidderminster Harriers, Moyes said: "We certainly did [get close to deals] but for different reasons it didn't quite happen.
"I'd never tell you my targets because that would be wrong even the names you are mentioning I could not guarantee if you were correct or not, but what I do want to do is be ambitious here at West Ham, I want to bring in good players and I want to add to what I think is a really good squad, we are building on it.
"Sometimes, getting things you actually want, you have to wait a little bit longer. We were not able to get it this January window. But I think it was quite obvious to most clubs, as I said I think it was nine clubs who didn't do any business in January, so it should be no surprise to a lot of people that we were one but we did try very hard I have to say."
When asked by reporters if the Hammers would attempt to sign Lingard next summer, Moyes replied: "I don't know, we will see."
West Ham are now focused on getting the job done away at Kidderminster this weekend, as they bid to reach the fifth round of the FA Cup for just the second time in the last six years. body check tags ::