Tomlinson, a lifelong fan of the League 1 club, said he was "absolutely gutted" that the deal appears not to be going ahead, but said he still aims to help the club succeed.
In a message to fans posted online, Tomlinson said he insisted he would not benefit financially from the club if the deal had occurred.
The singer announced last month, after weeks of speculation, that he was teaming up with businessman John Ryan and their takeover was expected to be formalised on Friday.
But efforts to raise enough cash for the deal - through the Crowdfunder.co.uk website - have faltered with only £757,796 of the £2million target raised by Thursday's deadline from 514 backers.
A statement issued on Thursday by the Tomlinson Ryan Trust, established by the pair, said the failure to reach their target meant they were unable to meet the Football League's 'fit and proper persons' test for club ownership
In a series of posts online, Tomlinson wrote: "I'm absolutely gutted the Doncaster Rovers deal is not going ahead. I am desperate for the club to be given the recognition it deserves.
"I was explicitly told that the deal to buy the club was not dependent on the money raised by Crowdfunding. Unfortunately I was misled.
.