My ranking, with the worst at the top, with the note that all of these pale when compared to 2007:
2010 loss to NYJ: This was hurts the most because it was a true lost opportunity to get back to the Super Bowl. The Jets were admittedly a decent team, but one that the Pats dominated just a few weeks earlier. The game as excruciating as the Pats simply executed poorly across the board. The one issue that season was the Pats defense was uneven; Green Bay made a game of it in Foxboro in a game the Pats won because Rodgers missed the game and backup Matt Flynn did not have experience with their 2 minute offense. And when the Pats finally scored a TD and 2 point conversion against the Jets to make a game of it at 14-11, the defense promptly gave up a 58 yard catch-and-run to Jerricho Cotchery to start the 4th quarter, missing tackles all over the place; the Jets would score a killer TD later on the series. What also hurts is that the Pats loss essentially assured the Steelers of making the Super Bowl.
2017 (2018 Super Bowl) loss to Philly: In many ways, this season was the inverse of this past season. After their typical 2-2 start, the Pats started to click once again. However, the injuries were like a slow drip that occurred throughout the year: they lost Edelman, Cyrus Jones, and Derek Rivers in training camp. Super Bowl hero Malcolm Mitchell never recovered. Martellus Bennett was brought in and promptly got hurt. Marcus Cannon and Donta Hightower were lost mid-season. Hogan had a bad concussion mid season and never really returned to form until the Super Bowl. Burkhead was in and out all season. Jonathan Jones got hurt in the playoffs. Gronk probably shouldn't have played in the Super Bowl to be honest. But the worst had to be the constant second guessing that happened in the aftermath. The other reason this one ranked high is that it was a chance to repeat.
2011 (2012 Super Bowl): In normal situations, this loss would not be ranked that highly. The AFC was weak that year; the Steelers lost in the playoffs to Tim Tebow. The unstoppable combination of Brady, Gronk, Hernandez, and Welker and a soft schedule helped mask both a weak running game and an atrocious defense. The Ravens outplayed the Patriots during the AFCCG and probably would have won had they not fell victim to some curious play calls by the Ravens offense during the final 2 drives and missed chip shot FG by Cundiff. The Giants team was in some ways similar to this season's Pats team: after tough mid-season stretch where they lost 4 in a row and 5 of 6, they turned it around and won 2 to close out the season, and then ran through the playoffs, beating Alex Smith and the 49'ers in OT to earn their trip. But what hurt is that this game was against the Giants and Eli f-ing Manning. And they way they loss was painful; first there was that bizarre intentional grounding call in the end zone against Brady. Still, the Pats had a 17-9 lead early in the 2nd half. Then the D lets the Giants march down the field for two FG's (albeit one of those drives was on a short field). Then the Pats have a promising drive get cut short with an awful Brady INT. Then the Welker drop on a play that would have likely iced the game. Then the circus catch by Manningham, which was followed by the Pats D showing their ugly side by allowing Manning to easily complete 2 more big passes against the cushion of doom.
Anyway, those are the top 3. In case you're wondering, the 2006 loss in the AFCCG would get an honorable mention. However, that one has eased up over time. The Pats were playing over their heads to some extent, and may have had a more difficult time in the Super Bowl then most people here would expect. IIRC, the Pats lost Richard Seymour that game, and then Troy Brown hurt his knee while trying to catch a pass that would have iced the game for New England. Maroney had gotten hurt late that season and never seemed to return to his earlier season form, and Dillon was clearly cooked.
The other remaining losses, while they sting, were simply cases where the Pats got beat plain and simple. The 2015 Pats defense was nowhere near as good as the 2015 Broncos D. Maybe if the game was in Foxboro, the result would have been different, but good teams can once in a while win in Foxboro as well, so who really knows. Teams with good defense can win tough playoff games on the road (like the Pats just did in KC). And the other Pats teams simply were not as good as the teams that beat them.