A January loan arrival from Manchester United, Antony has been a revelation in a Betis shirt.
The deal doesn't include a permanent option, but Fajardo has made it clear they want to keep the Brazil international.
He told Estadio Deportivo: "It is a source of satisfaction on a personal level (having brought Antony to Betis), but it is the result of teamwork.
"Although I am responsible for the sporting management, there are many people involved in this signing. It is still early days, but we will try, in different ways, to do everything to continue enjoying Antony."
Real Betis, meanwhile, have hopes of winning the Europa Conference League.
Fajardo added, "We are one of the few Spanish teams that are in two competitions, on the verge of a quarter-final, and for us it means a lot to be able to be in the semi-finals of a European competition."