The 22-year-old, who has started all four of the Cod Army's matches this season under the tutelage of former Ibrox midfielder Joey Barton, was replaced at half-time. He had left the pitch during the first period for treatment and resumed play with his head bandaged, but did not emerge for the start of the second 45.
Speaking to the Scotsman's sister title, the Blackpool Gazette, Barton revealed why the former Liverpool youngster had been unable to continue, despite setting up Conor McAleny for the opening goal.
“We scored a goal and Jordan had to come off. He got a cut to his eye, which was caused in our celebration, weirdly," Barton said.
“Hopefully it is nothing to worry about and he is available for selection [against Wycombe Wanderers tonight].
“He was off the pitch for a period [receiving treatment] and we did not get a chance to enjoy our 1-0. In that period it was men against boys."
Fleetwood went on to lose the League One game 3-2, despite Rossiter's replacement Paddy Madden levelling the scoreline after Cameron John and James Coppinger had put the home side in front.
An injury-time own goal from former Aberdeen loanee Wes Burns handed Donny their first win of the new season.
There was plenty of Scottish interest in the Fleetwood Town squad aside from Barton and Rossiter, with former Dundee United and Ross County defender Harry Souttar starting in defence while ex-Aberdeen and Cove Rangers midfielder Paul Coutts also lined up for the Lancashire side.
Conor McAleny, who spent time on loan at Kilmarnock last season, started up front and scored the opener.
Rossiter and Barton's former Ibrox colleague Matt Gilks was named on the bench alongside ex-Celtic and Scotland forward Ross Wallace.