Rovers were reportedly targeting Nottingham Forest's Lewis O'Brien and Rochdale's Ethan Brierley but failed to complete the deals in time.
A club statement on Blackburn's website said: "One of the deals was a very ambitious target and it was only confirmed that he was able to join us late Tuesday afternoon.
"Despite the club's best endeavours to complete all the required elements of this loan transfer, due to events we believe to be outside of our control, the deadline for submission was late and despite the club stating the mitigating reasons for the delayed submission, our application has today been rejected by the EFL.
"Our application for the second deal - for the permanent transfer of a promising young player - was also delayed due to unsigned paperwork and technical issues encountered by the club at the point of submission.
"Once again the EFL has not accepted these issues were an impediment to the paperwork being lodged on time and has also rejected this application.
"The club will now appeal the EFL decision to reject both applications and will submit documents ahead of the Tuesday, February 7 deadline."
Jon Dahl Tomasson's side sit sixth in the Sky Bet Championship and face Wigan on Monday evening.