He also revealed that during his time as assistant manager between 2014 and 2016, he clashed with then Dutch manager Louis van Gaal over the sale of players.
Jesus joined Manchester City for a reported £27 million in January while Mbappe swapped Monaco for Paris Saint-Germain this summer, initially on loan but with an option to make the move permanent next summer for a fee of around £166 million.
'I watched Mbappe for a year.
"You can't just go gung-ho against every team, especially when I don't think the players are outstanding like they have been in the past", he said.
"It would have been £5 million ($6.7 million, 5.7 million euros) or something - get them, loan them back - and that's where the recruitment could have been better".
Giggs also said that United should not have sold players, including defenders Rafael Da Silva, Jonny Evans and striker Danny Welbeck, who were used to the club's style of play under long-serving former boss Alex Ferguson.
Giggs says United passed up chance to sign Jesus, Mbappe
"He understood because I had played with those lads, but they just weren't for him".
Jose Mourinho's United side have been oft-criticised for a boring style of football, despite being the second-highest scorers in the Premier League this season.
"They had fallen down the pecking order, so do they go for someone who - and it winds me up saying this - hasn't got experience as a manager or do they go for a victor?" said Giggs.
"I do feel I would be more suited to coaching at the top than coaching at the bottom". I know now I wasn't ready when I had those four games in charge at United [as caretaker in 2014], but I'm a lot better qualified to manage now after those two years with Louis.
"I know what a Manchester United player looks like", added Giggs.
"I don't have experience in the lower divisions. That was a fantastic experience".
"I totally understand that". Gary Speed and Chris Coleman didn't have much experience when they got the job.