Sinclair and Barnett were two of four players fined and transfer-listed following an alleged incident in Peterborough city centre on Saturday night and Evans made his move within one hour of the news breaking.
Sinclair was primed to join the Millers on loan earlier on in the season and Evans signed Barnett at Crawley so the Millers boss has history with both, but his attempt was refused after Posh told him the duo were only available for permanent transfers.
"I spoke to Tyrone when the news broke and he is devastated," Evans said.
"They're players we would love to bring here, but we can't afford them. I spoke to Peterborough within an hour asking about loan moves but they are only available for permanent deals.
"It's about affordability and desire. Would they want to come to League Two when they see themselves as Championship players?"