Berbatov's spot-kick was particularly disappointing with a tame, lazy effort, as he had the chance to put his side in the driving seat after Tim Cahill hoofed his side's first penalty over the crossbar.
After the rest of the penalty-takers held their nerve, it was down to Jagielka to complete a famous victory, propelling the Blue half of Merseyside into a first major cup final since 1995, when they defeated Sir Alex Ferguson's team to lift the FA Cup at the old Wembley.
United fans will be left to wonder why eight changes were made from the side that defeated Porto in midweek, but with the games coming thick and fast, the Old Trafford boss was obviously forced to rest some of his exhausted talent.
Two hours of tense football were dominated by defences as the likes of Nemanja Vidic, Ferdinand, Jagielka and Joleon Lescott were firmly on top of their opposition's attack.
Chances were slight as well as being few and far between, as both sides struggled just as Arsenal and Chelsea did on Wembley's bobbly surface.
The main attacking threat from United came from the likes of first-team regulars Anderson and Carlos Tevez, as both South Americans often worried the Everton defence with decisive and direct dribbling.
However, Italian super-kid Federico Macheda and Danny Wellbeck struggled to provide any significant prowess going forward and the Everton back four were comfortable throughout.
The main talking point of the game came midway through the second period. Jagielka appeared to hack down Wellbeck from behind without taking any of the ball just inside the Everton box, but referee Mike Riley ignored the claims for a penalty, incensing Ferguson in the process.
Both defences prevented any clear-cut chances as both sides tried to score from distance as the match moved into extra-time.
The one and only big chance of the game fell to Everton substitute James Vaughan, who mishit a cross in space after a clever run from the excellent Leighton Baines.
Both sides appeared to run out of steam in the last 15 minutes of extra-time, signalling the shootout and eventually an end to United's quest for a historic five trophies in one season.