Much of the pre-match build-up had centred on Shelvey's first appearance against the Reds since his summer move to south Wales, and he made a dream start as he fired the home side ahead after 87 seconds.
But just 99 seconds later his woeful backpass allowed Daniel Sturridge to equalise, and another misplaced pass saw Victor Moses put the Reds ahead on his debut.
Shelvey was left with his head in his hands and the visitors led 2-1 at the break, but he responded by teeing up Michu for an equaliser with a surging run and astute cushioned header.
Laudrup praised the 21-year-old's character, but admitted he had a word with the ex-Charlton man at the interval.
"It was a difficult half for him," he said.
"But I said 'there is no problem, go out there, you still have 45 minutes to turn it around'.
"He knew only he could bring himself back into the game and it was a fantastic reaction to pull himself together.
"It says a lot about him, he is still very young and he will be stronger for this game."
Shelvey apologised to the Swansea fans after the game, telling Sky Sports 1: "I just want to say sorry to the Swansea fans for two bad mistakes.
Source: PA
Source: PA