West Ham signed Fonte from Southampton and Snodgrass from Hull in January 2017.
The London club paid the Tigers a transfer fee of £10.2m for the 30-year-old Scotland international winger, as reported by BBC Sport.
In a recent interview with The Guardian, West Ham co-chairman David Sullivan suggested that he did not want to sign Fonte and Snodgrass.
The manager said he wanted Fonte from Southampton and Snodgrass from Hull,” Sullivan told The Guardian. “My kids begged me not to sign them.”
Bilic, who was appointed the West Ham manager in the summer of 2015 and parted company with the Premier League club in November, has explained why he signed Fonte and Snodgrass.
“I am not going to take credit for everything but I don’t want to take all the blame either,” Bilic told The Daily Mail. “Fonte and Snodgrass came in January.
“We were losing Payet and Ogbonna was having an operation, and of course the budget was limited. So we got those two new players.
“To criticise them is unfair. They came to a club in a difficult situation and helped us finish 11th so they played their part.”
Fonte is injured at the moment, while Snodgrass joined Championship club Aston Villa on a season-long loan deal in the summer transfer window.