But at this point, the 5-8 Eagles are in desperate need of "W's" any way they can get them.
"I'm happy for our guys because they worked their [butt] off," Castillo said. "And when you work your [butt] off and you win, you get rewarded. . . . The thing that happens is when you don't get rewarded and you work your [butt] off, you start losing faith."
Many had come to the conclusion that the Eagles, especially Castillo's charges, had lost their confidence after two lackluster performances against the New England Patriots and Seattle Seahawks. But somehow they were not mathematically eliminated from the playoffs heading into this weekend and that's how they will remain at least for another week.
The Eagles still trail the Dallas Cowboys and New York Giants, who are tied atop the NFC East at 7-6 after the Giants' 37-34 win over Dallas Sunday night. And the Eagles are still, by the smallest of calculations, alive in the wild-card race. But the challenge remains the same: They have to win out to have any chance at reaching the postseason.
"We still believe," said cornerback Asante Samuel, who forced and recovered a fumble on Sunday. "This is the start of our new season."
It's hard to erase what occurred during the "old" season, though. But the fact that coach Andy Reid was able to still muster a strong effort from his team, despite evidence from the previous two games that he may have lost some of his players, could make his return next season a foregone conclusion.
"I think in order to win, you have to have great effort," Reid said. "You're not going to beat a good football team without the effort."
Relatively speaking, the 4-9 Dolphins aren't good. But they did win four of five coming in, and jumped out to a 7-0 lead early in the first quarter. But those points came courtesy of a blocked Chas Henry punt and a Brandon Marshall 16-yard touchdown reception on Miami's ensuing possession.
Other than that score and a 22-yard field goal in the third quarter, the Eagles manhandled Miami. The defense forced three turnovers, recorded nine sacks and was stout in short-yardage situations. The Dolphins were successful on only 3 of 15 third downs and failed on all three of their fourth-down attempts.
"If you would have said ahead of time what we were going to do on third down [and] short, fourth and short, everyone would have said, 'You're crazy,' " defensive end Jason Babin said.
Babin, who now has 15 sacks on the season, notched three Sunday, as did defensive end Trent Cole. But the defense's biggest contribution was turnovers.
"My hat's off to the defense. The defense [stood up] today," Eagles guard Todd Herremans said. "If they didn't come up how they did, I don't know if we win this game."
Safety Kurt Coleman intercepted Matt Moore in the second quarter, setting up a LeSean McCoy 2-yard touchdown run, his second of the game. Samuel's fumble recovery led to a field goal. And Babin's strip of Moore not only offset a boneheaded trick lateral on a punt that led to a fumble, but it was turned into another seven points when Michael Vick hooked up with DeSean Jackson for a 34-yard touchdown.
It was Jackson's first touchdown since Week 5 and only his third on the season.
"I'm proud of DeSean, with everything that he's been faced with this season," Vick said. "He's just a guy that wants to play good football, now that all the distractions are out of the way."
Vick, back after a three-game absence, and the offense were able to turn those three turnovers into 17 points, but the group was ineffective for much of the day.
"That was a pretty good first half offensively, and just horrendous in the second half," Eagles offensive coordinator Marty Mornhinweg said. "We've got some work to do."
But converting Miami's giveaways into points gave the Eagles a comfortable lead and the Dolphins were forced to rely on their anemic passing game. And when left tackle Jake Long left with a back injury, Cole, Babin and company were able to tee off on Moore and backup J.P. Losman, who took over after Moore left with a concussion.
"I can't use the words the D-line uses, so we have to say devastating," Castillo said when asked to describe the pass rush. "That's probably a good word."
Little-used defensive end Phillip Hunt provided the final tally - and the Eagles' only second-half points - when he sacked Losman in the end zone for a safety.
At that point the stadium favored Eagles fans, many of whom had traveled from all across the country, much as they did the last time these two teams met here in 2003. Four of the Eagles' five wins have come on the road.
They return to Lincoln Financial Field to face the New York Jets on Sunday and, of course, the prospect of boos and "Fire Andy!" and "Juan must go!" chants should the Eagles revert to form.
But they left Miami to cheers, and that was good for now.
Contact staff writer Jeff McLane at 215-854-4745, firstname.lastname@example.org or @Jeff_McLane on Twitter.