Neither Chad Henne nor Tyler Thigpen could do much with the offense as Miami fell behind 38-0 before a late touchdown helped the team avert its second shutout of the season.
"We don't want to be in this position again, and we shouldn't forget what just happened to us out there," said Sparano, who looks forward to meeting with Ross and sharing his ideas for improving the Dolphins. "It's not a good place to be, and we did it to ourselves."
Sparano, who has one year left on his contract, led the Dolphins to the playoffs in 2008 -- his first season as an NFL head coach -- for their only postseason appearance since 2001. But Miami is 14-18 since then.
"He is such a good coach," Dolphins cornerback Benny Sapp said of Sparano. "You just hate to see it go down like that, especially when (he) works so hard during the week getting us motivated."
The Patriots (14-2) already had clinched home-field advantage through the AFC playoffs, and the Dolphins had long been eliminated from postseason contention. But Miami (7-9) came into Sunday's game with a chance to finish .500 and end the season with a win that could help make the case for keeping Sparano.
The Associated Press contributed to this report.