Hull KR's Paul Cooke heads for the try line during their match against Bradford at Craven Park
Galea limped off in the early stages and was immediately replaced by Chaz I'Anson and is now rated doubtful for the season opener against Salford on February 7.
Bradford's Craig Kopczak broke a leg, meanwhile, and will definitely miss the start of the season.
Despite the Galea injury and the result, Rovers can take some positives from the game with Peter Fox and Mick Vella getting plenty of game time.
Both were making their first appearance of the pre-season.
Fox did well with the small amount of possession he had, while Vella blew away a few cobwebs with a solid show in the middle of the pitch.
For Rovers, Paul Cooke had a very good game running the ball more in any game he has played for the Robins and that included returning a restart.
Cooke opened the scoring in the 10th minute after taking the line on and spinning his way out of trouble for the try. Michael Dobson's kick made it 6-0.
After soaking up a lot of early pressure, Bradford drew level in the 24th minute when Michael Worrincy went over after Matt Orford's kick through was deflected into Worrincy's path.
Four minutes later Stuart Reardon doubled Bradford's lead, sliding over in the left-hand corner. Sykes kicked both goals as the visitors led 12-6.
It took a while for Rovers to get going and they deservedly drew level in the 53rd minute when Clint Newton cleverly knocked down Dobson's cross-field kick into I'Anson's path for a well worked score. Dobson's kick made it 12-12.
Bradford went in front again in the 65th minute when Orford's delayed pass to Elliot Whitehead froze the Rovers defence. Sykes kicked his third goal to leave Rovers six points adrift with 15 minutes remaining.
With time running out, Rovers threw caution to the wind and scored in the final minute with the best move of the game. It started on the right with Michael Ratu's run and offload.
After two more offloads and with the play now moving down the left-hand side, Kris Welham finally grounded the ball out wide. Dobson missed the kick giving Bradford a narrow 18-16 win.
Other positives for Rovers were Shaun Briscoe, who after a couple of unusual errors in the first half, bounced back to finish the game strongly.
His take under pressure in the 74th minute was Briscoe at his best. Dobson had another solid game, while Scott Murrell's tackling and Ben Cockayne's tenacity were impressive.
Rovers finished the game with Murrell at loose forward and Josh Hodgson at hooker.
If Galea doesn't make it in time for the Salford game, that could be the way Morgan starts the season. With the friendlies now complete, Morgan will use the next nine days finalising his game plan to face Salford.