Pascal Chimbonda's miss after 120 minutes and 13 penalties was the final blow to Spurs' hopes of progressing to the UEFA Cup quarter-finals.
Chances were few and far between in a slow-paced opening 45 minutes. With PSV happy to sit deep and Spurs, initially at least, content with a patient game, a goal feast was always unlikely.
Tottenham had to wait 17 minutes before they were even given enough space for a shot.
Steed Malbranque collected the ball 12 yards from goal and, despite having yards of open grass ahead of him, the Frenchman rushed his shot, firing well over the crossbar.
Little more was created by either side and it was no surprise when, at half-time, striker Darren Bent came on for Spurs' left-back Young-Pyo Lee.
Bent's first touch almost produced a goal, his mis-hit shot from ten yards forcing a save from goalkeeper Gomes, a move which kick-started a dominant 45 minutes from the English side.
PSV had their chances, with Danny Koevermans completely missing a lobbed pass which saw him given onside despite the entire Spurs defence stepping up and leaving him free.
Eventually the skill and patience shown by Spurs paid off as Berbatov fired in a brilliant volleyed goal after 81 minutes to send the game spiralling towards extra-time.
The attacking intent shown by Spurs in the second half fizzled out as both sides hung on for a penalty shootout - although Gomes had to tip over a 120th minute strike from Malbranque.
Gomes took this form into the shoot-out, saving brilliantly from a Jermaine Jenas penalty that would have won the game for Spurs.
Yet in the end it was the nerves of Spurs right-back Chimbonda that won the game for the Dutch side, giving another English club the boot out of Europe in a bad day for the Premiership's continental adventurers.