Beck's Third Division side who knocked out Manchester City in the second round, were given a ninth-minute lead by Gareth Ainsworth and had Southampton in trouble with their direct style But just when it seemed that the second- half heroics of the Lincoln goalkeeper, Barry Richardson, would secure another famous scalp, Southampton won a 75th-minute penalty and Jim Magilton scored the equaliser.
Lincoln's stubborn resistance began to crumble and the substitute Gordon Watson pounced to put Southampton ahead six minutes from time. Eyal Berkovitch, the club's recent signing, added a third in the last minute and Lincoln's Cup run was over leaving Beck to ponder over what might have been.
Beck felt Chris Woods' fingertip save to keep out Gijsbert Bos' header five minutes after Ainsworth's opener and Saints' penalty, awarded for a Jason Barnett trip on Egil Ostenstadt, had been the major turning points of the tie.
"If we had scored another when we were 1-0 up, and we had a few chances, they might have been dead and buried, but it wasn't to be," Beck said.
"I'm disappointed with the ref's decision on the penalty. It was a very harsh decision and it turned the game. We were keeping them at bay and then suddenly, out of nothing, the penalty got them back in it. It's left me feeling very empty."
Beck's disappointment at the way in which the replay, earned by Lincoln's 2-2 draw at the Dell three weeks ago, had slipped away from his side was tempered by the knowledge that Southampton had been given a rough ride.
"We put the frighteners up them," Beck said. "We've done extremely well to get this far and to be disappointed at getting beat by a Premiership club.
"We've had four Cup finals for little Lincoln and there are 23 other Third Division sides who would have loved to have been in our shoes. We're very proud of that."
The Southampton manager, Graeme Souness, felt a mixture of pride and relief at the way his side stuck to their task after losing an early goal and trailing deep into the second-half.
"We didn't panic or change our style," Souness said. "We kept passing it and that's what got us the opportunities to get back into it.
"It would have been a difficult game for anyone coming here but I thought we handled it well.
"The danger, when you play these sort of games, is that you end up playing like them. It was important that we continued trying to pass the ball and we did.
"As the game went on they dropped off a bit and we came into it more. When their keeper saved Matt's (Le Tissier) free-kick I thought `maybe it's going to be their night' but once we got the first goal I felt we'd go on to win it."
Southampton's victory has earned them another potentially awkward tie away to Oxford United.Reuse content