Shelvey gave the ball away twice in the first half, allowing Daniel Sturridge and then Victor Moses to put Liverpool 2-1 ahead at the break - cancelling out his own second-minute opener.
The 21-year-old's eventful reunion with his former club continued when he set up Michu for the equaliser after the interval, but he was downbeat afterwards.
"I just want to say sorry for the two bad mistakes that gifted Liverpool the goals," Shelvey told Sky Sports.
"You just want to go into a hole where nobody can see you but football is about coming back.
"It's just a horrible feeling that you don't wish on anyone, not even your worst enemy, but it's football at the end of the day.
"I feel like I've given Liverpool a draw but it was a great game to play in."
Swansea boss Michael Laudrup was delighted with how his side performed in the second half, as they moved up to 13th in the Premier League.
"It was a great performance in the second half after a very difficult first half," he added.
"We had to perform better in the second half and the boys did an excellent job."
However, Laudrup revealed that he had to pick up a disheartened Shelvey at the break after his mistakes helped put Liverpool on top.
"Of course, when you do that you go from heaven to hell in a couple of minutes," he continued.
"He's only 21, but I said, 'Come on, you have to learn from this', and I think he did great.
"He will come stronger out of this because his reaction to what happened was excellent."
