Vicky Jepson’s side played some excellent football in the fifth round tie at Prenton Park as popular defender Satara Murray played her final game in a red shirt.
Millwall Lionesses might be one division below the Reds in WSL 2, but they came with a plan and frustrated the Reds in a goalless first-half.
Jepson’s team had most of the possession but try as they might they couldn’t find an opening.
Linnett and Niamh Fahey both saw efforts disallowed for tight offside calls, and visiting goalkeeper Chloe Sansom made some fine saves to deny Babajide and Courtney Sweetman-Kirk.