Backup quarterback Deon Anthony ran for two touchdowns and was 9-of-12 passing for 93 yards and a score for the Trojans (5-5).
Troy (5-5) has two games remaining in its regular season.
"That's what we've been told, but we're going to get to seven (wins)," Robinson said. "That's what we're shooting for."
The Trojans scored on their first three possessions and led 21-0 early in the second quarter.
"We never seemed to recover," Navy coach Ken Niumatalolo said. "You have to give them credit, and I'll take the hit for this. Obviously, they were more prepared than we were."
Gee Gee Greene ran for 150 yards and a touchdown, while quarterback Keenan Reynolds had three rushing touchdowns for the Midshipmen (6-4), who had a five-game win streak snapped.
Reynolds finished with 128 yards rushing and was 8-of-15 passing for 159 yards.
Troy, a week after totaling 721 yards in a 55-48 loss at Tennessee, had 597 yards Saturday. The Midshipmen (6-4) finished with 487 yards, including 328 rushing.
"They've scored a lot of points against a lot of people," Niumatalolo said. "We didn't play our best out there."
Anthony threw a 34-yard touchdown pass to Chandler Worthy on Troy's first drive. Shawn Southward added a 6-yard TD run and Robinson had a 62-yard pass to B.J. Chitty, giving the Trojans a 21-0 lead early in the second quarter.
Reynolds had second-quarter touchdown runs of 5, 5 and 1 yards. Anthony also had a 44-yard TD run and Troy led 28-21 at halftime.
Navy sliced Troy's lead to 31-28 in the third quarter on a 59-yard touchdown run by Greene. Early in the fourth, the Trojans pushed the lead back to 10 points with Anthony's 4-yard TD run.
After Navy's Nick Sloan kicked a 27-yard field goal to make it 38-31 halfway through the final period, Troy answered with an 11-play, 69-yard drive. It ended with Will Scott's second field goal, a 23-yarder with 3:09 remaining.
"It was all about us being more disciplined than them," Troy defensive back Bryan Willis said. "That's what it came down to."
Navy falls at Troy, 41-31
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