United snared Lukaku from Everton in a move reportedly worth an initial £75 million on Monday, the striker signing a five-year contract with an option of a sixth.
The deal came after the Belgium international had seemingly been set for a return to former club Chelsea for much of the transfer window, while Mourinho's men had pursued Real Madrid star Alvaro Morata.
Lukaku's move to Old Trafford caught Neville by surprise and he feels United stopping their Premier League title rivals from improving – particularly with Diego Costa expected to leave – played a part in Mourinho's decision.
"It caught me by surprise, I thought they were going to go for Morata and Jose said they actually bid for Morata," Neville said to talkSPORT .
"What Jose likes in all the teams he has managed is a target man and if Diego Costa leaves Chelsea you think maybe Jose was stopping Lukaku going to Chelsea to make them stronger as he is probably the best target man around."
Neville also believes Everton, his other former club, have had an impressive transfer window, tipping Wayne Rooney and Sandro Ramirez to shine at Goodison Park to help fill the void left by Lukaku.
"It [the Lukaku deal] is good for both clubs," he said. "Everton have got unbelievable money, invested that money really well, and I think both parties will be happy.
"What Everton have done really well – and they probably haven’t had the clout in the past to do – they have got the players in so that when they have to sell a player, the fans are still happy. They have five or six quality players in and are still going to bring in another two.
"I think on paper they could have got the snip of the season so far in Sandro. I watched him a lot last season for Malaga. He is fantastic, his movement is brilliant, he is young and a Spain Under-21.
"I think there are massive things to come from Wayne Rooney. He is Everton through and through. People think he is going there just to retire. He is only 31.
"Having watched him over the last 12 months and the lack of match action he has got, this could be the move that gives his career a kick on – you need it at that age."