The Hammers played out a 1-1 draw with Premier League rivals United away from home at Old Trafford in the fifth round of the FA Cup last weekend.
France international attacking midfielder Payet scored in the 68th minute with a stunning free kick that United goalkeeper David de Gea failed to keep out.
Bilic has admitted that he did not expect the former Marseille star to score with that effort.
“On Sunday I was expecting him to shoot but as Dimitri lined it up I was thinking that it was a bit far out and David de Gea is in goal - one of the best,” the West Ham boss wrote in The London Evening Standard.
"I said to myself, ‘this has to be a great one’ - and it was. It was one of the best but to be fair, I am not objective.”
Payet, who joined West Ham from Ligue 1 outfit Marseille in the summer of 2015, has been one of the best players in the Premier League this season.
The 28-year-old attacking midfielder has scored eight goals and created 79 chances in 22 Premier League appearances so this campaign.
The Frenchman has a pass accuracy of 82% and a shot accuracy of 65%, and has won two headers, 55 dribbles and 13 tackles.