Swansea midfielder Jonjo Shelvey apologised to City supporters after his mistakes set up both Liverpool goals in the 2-2 draw at the Liberty Stadium.
Shelvey put the Swans ahead against his former club, before his slack backpass allowed Daniel Sturridge to equalise.
Victor Moses put the Reds ahead after a sloppy pass by Shelvey, who made amends by setting up Michu's leveller.
"I just want to say sorry to the fans for the two bad mistakes that gifted Liverpool a draw," said Shelvey, 21.
"You just want to go into a hole where nobody can see you when you give the ball away for the other team to score, but it has happened to great players over time."
The England international was making his first appearance against Liverpool since leaving Anfield in a £5m summer move.
He showed composure to curl in Swansea's opener after 87 seconds, before his lack of concentration allowed Liverpool to level less than two minutes later.
The visitors led before half-time when another wayward pass from Shelvey was seized upon by Reds debutant Moses.
But the former Charlton man partially redeemed himself by flicking on a Leon Britton pass for Michu to steer in a second-half equaliser.
"I showed a bit of character to keep getting on the ball," added Shelvey. "I still feel I have given Liverpool a draw but it was a great game to play in."
Both Swansea manager Michael Laudrup and Liverpool counterpart Brendan Rodgers have backed Shelvey to learn from the experience.
"When you do that you go from heaven to hell in just a couple of minutes, scoring a goal in a very important game for you after two minutes but then you give away a goal - and another one with a ball lost," said Laudrup.
"I told him [at half-time] 'there are still 45 minutes, you have to learn from this and pull yourself together', and I think he did great.
"He will become stronger out of this, his reaction in the second half was excellent."
Reds boss Rodgers added: "Jonjo Shelvey is an outstanding young player, but he knows he has things in his game he needs to improve on.
"He will only do that from playing. This was a steep learning curve for him."