The Brazil international joined Ole Gunnar Solskjaer’s side on deadline day, with United agreeing a £15.4 million deal with the Portuguese club.
Porto’s president claims the left-back was offered ‘compensation’ to remain at the club until his contract expired next summer.
But the 27-year-old was desperate to complete his switch to United.
‘There are times when we have no other solution,’ Da Costa told O Jogo.
‘A week or two earlier, Alex’s sister, who’s the agent, expressed his desire to leave.
‘A week before the market closed, he asked to leave because he really wanted to go to Manchester.
‘I tried not to let him go, I tried to compensate him, even if it was to stay until the end of the year.
‘But it’s not possible to keep a player who takes over publicly and before me and my management he wanted to leave.
‘I tried to contradict because he is currently in the national team.’