Downing completed his move back to his hometown club Middlesbrough from the Hammers after signing a four-year contract on Thursday.
The 30-year-old winger, capped 35 times by England, will cost Boro £5.5m, although that could rise to £7m if they are promoted from the Championship.
Bilic says he would rather have kept Downing in his squad, but did not want to prevent him from returning home.
“I didn’t want him to go, he’s a quality English player and I know how hard it is to get the quality ones,” said former Croatia boss Bilic.
“Of course I rate him, I tried to persuade him to stay with us.
“I know him from the national team when we played England, and he was brilliant in the first half of last season. I was counting on him big time, but he told me that he wanted to go home.
“He said, ‘I like you and everything, but I want to go home. If it was any other club, I would stay here’.
“Maybe I could have stopped him, and all that, however it is not what we wanted to do, but he wanted to leave.”