The midfielder fluffed an injury-time spot-kick that cost Crystal Palace three points on New Year’s Eve but he made amends on Tuesday.
Milivojevic sealed victory by scoring late on with a brilliant shot from the edge of the area as Palace came from behind to continue their impressive form under Roy Hodgson.
“I have to be honest, I did not sleep the past two nights,” said the Serbian after his winner moved Palace up to 14th in the table and two points clear of the relegation zone.
“It was very hard to miss in the last minute, especially because it was against Manchester City and it was in our stadium.
“Thank God, I scored and the team won. I am so happy. I will sleep much better now, that’s for sure.”
Milivojevic had scored all of his first five penalties for Palace but his poor effort against City was saved by Ederson in the goalless draw at Selhurst Park.
“I have to thank my team-mates,” he said. “They gave me support. No one said anything negative. I scored five in a row. I missed one and that happened only because I changed my decision.
“I did not feel big pressure. I wanted to shoot in the middle but I shot badly.I also have to say a big thanks to the fans for their support. After I missed, they were singing my name and they gave me enormous support.”
Palace have lost just once in 11 matches and are now three points off the top half of the table after they produced a good comeback in difficult weather conditions.
Shane Long put Southampton ahead in the first half but James McArthur equalised before Milivojevic curled home an effort from 25 yards.
“I tried to forget about the penalty but it is not easy,” Milivojevic added. “We needed these points. Against City, we had a great effort and ran a lot to try to stop them and to get some points. I am very proud of the team. Once again, we showed character.”
Palace’s win was marred by the news that Scott Dann and Jason Puncheon will miss the rest of the season with knee injuries.
Both players suffered cruciate knee ligament damage against City in separate tackles on Kevin de Bruyne, who had recovered from the heavy challenge by Puncheon to start against Watford last night.
Hodgson confirmed after the game that Puncheon and Dann each face a long spell out and could even miss the start of next season.
Asked if Palace will now look to sign a central defender in the January transfer window, Hodgson said last night: “It is too soon to say. We have just come to terms with the news. We did not know until today it was definite that Scott has injured his cruciate.
“The chairman [Steve Parish] and the American directors [Josh Harris and David Blitzer] are very keen to improve our squad.”
Palace play Brighton in the FA Cup on Monday and Hodgson has suggested he will make changes for the third-round tie and rest players at Amex Stadium.
Hodgson said: “The fans might not like to hear that I am hoping to freshen up the team. One or two players need to breathe after these 11 games and get their head right for the last 16.”