Moyes, who was announced as Sir Alex Ferguson's successor at United in May 2013 made Germany international Kroos a priority target after taking over.
Moyes claims that Kroos, who had two years left on his Bayern Munich contract, told him that he would join United, before changing his mind.
"Toni Kroos had agreed to come to Manchester United with me," Moyes told talkSPORT.
"I met him and his wife and we agreed it all when he was at Bayern Munich.
"It was hard for both of us at the same time," Moyes admitted. "In hindsight, if Ed Woodward had a year to work with Alex Ferguson it would probably have helped Ed Woodward.
"If David Moyes had a year to work with David Gill, I think it would have helped David Moyes as well at Manchester United.
"Overall it was a tough job for both of us to take over. They were both new jobs and [we were] following really good people."
After missing out on Kroos in 2013, United turned to Cesc Fabregas, who was then at Barcelona, but were unable to do a deal despite making multiple bids