Elizabeth Power and Kilpatrick River.
"She had a small bleed to the right side of her brain and had bruising to the other side," Robbie said.
"She is in a normal neurological ward at the hospital but will be under observation for 48 hours.
"The doctors are not worried about her but she is very sore."
Ireland's Joseph Murphy finished best of the Irish in 27th place in his Badminton debut.
Riding Kevin Monroe's Irish bred Cruising gelding Electric Cruise, the 35-year-old went clear in the showjumping to move up eight places from his overnight position.
Ninety-two combinations were selected to compete at theBadminton Horse Trials this year, and 56 finished all three phases.
The overall winner was New Zealand's Mark Todd and NZB Land Vision.
Other Irish finishers were:
45th Michael Ryan/Old Road (ISH) 84.1
48th Aoife Clark/Master Crusoe (ISH) 89.0
50th Louise Lyons/Murphy's Miracle (ISH) 94.4
53rd Mark Kyle/Step In Time 109.2