The former Reds midfielder scored the opening goal for his new club in the second minute before he unintentionally set up ex-teammate Daniel Sturridge with a poorly hit backpass for a leveller two minutes later.
Shelvey then played a subpar ball which allowed Liverpool loanee Victor Moses to give the visitors the lead after the half-hour mark before the England U21 international set up Michu for the equaliser with 25 minutes remaining.
Despite contributing to the Swans' two goals, Shelvey said he felt horrible for giving up two easy goals as his new side moved up to 13th on the Premier League table.
"I just want to say sorry to the Swansea fans for the two bad mistakes that have gifted Liverpool a draw," Shelvey told Sky Sports.
"I really thought we deserved more than that. It started tremendously, getting the goal, but then two poor mistakes.
"I showed a bit of character to keep getting on the ball, and I set the next goal up, but I'm still disappointed.
"I didn't really want to celebrate [after scoring] because I've huge respect for the Liverpool fans and I loved every minute being there, but it's hard to hide your emotions. Two minutes later, I give them a goal. It was good to score, but I can't stop thinking about the two mistakes.
"You want to go into a hole where no-one can see you. Football is about coming back from things like that and it has happened to great players.
"It's just a horrible feeling, I don't want to wish it on anyone, even your worst enemy, but that's football."