The bid was rejected by the football league after Louis and businessman John Ryan attempted to raise the money through crowd-funding.
"The situation is that the crowd-funder didn't succeed and we are very sorry about that but the real problem is with the Football League", said John.
Louis Tomlinson in his crowdfunder video
"They have made it so difficult now that unless you have a bag full of cash you are going to get turned down."
It was thought Louis and John would complete the takeover on Friday after signing the deal last month.
Mr Ryan reportedly claimed that the Football League wanted "cleared funds of £5M from day one", but he told BBC Radio Sheffield: "I told them I had assets well above that figure and it's just been disregarded."
Louis Tomlinson is a big football fan
It has been a long love affair between myself and Doncaster Rovers but it has hit the buffers today. The way I feel right now I doubt I will ever go to another football match in my life."
Louis and John, who have tried twice before to finalise the deal, chose to save their club after it was relegated to the third tier of English football in May.
Louis Tomlinson and John Ryan in their crowdfunder video
"For me, this is all about the football, the community and restoring the excitement and desire to making Doncaster Rovers the most exciting club to play for in Yorkshire," wrote Louis in a statement.
"I want to see the Doncaster Rovers supporters get the club the success it deserves. I grew up in Doncaster and have felt the love for football run through the town, it's for that reason that I have a real personal passion to make Doncaster Rovers a success story.
"This is a big step which I believe will open up opportunities to provide a very, very exciting future for the club and its supporters."