Carsley has been appointed on a temporary basis for Nations League fixtures against the Republic of Ireland and Finland next month.
Gareth Southgate stepped down in July after England lost the Euro 2024 final to Spain.
Chelsea winger Madueke, Lille midfielder Gomes and Nottingham Forest's Gibbs-White were all part of the England under-21 side that Carsley led to European Championship glory in 2023.
Newcastle full-back Livramento is included after his club team-mate Kieran Trippier announced his retirement from international football earlier on Thursday.
Real Madrid star Jude Bellingham is missing due to injury.
Manchester City's Kyle Walker was left out, alongside other Euro 2024 squad members Ivan Toney, Aaron Ramsdale, Joe Gomez, Lewis Dunk and Adam Wharton.
"It was important that I put my own stamp on the squad a little bit," said Carsley.
"We've been so close a couple of times (to winning major tournaments) and recognising that. But I thought it was important that we put some fresh faces in and put our own little mark on the squad."
Under Southgate England reached two Euros finals, a World Cup semi-final and quarter-final.
However, they have still not won a major tournament since the 1966 World Cup.
"I think the expectation now around the squad and the players is really exciting. So I understand that I'm in a really privileged position. One that I'm really looking forward to, I'm excited about it."
A lack of senior managerial experience could cost Carsley the job on a more permanent basis as he has limited experience from caretaker spells at Coventry, Brentford and Birmingham.
But he has been part of the England development squads in various roles since 2015.
"For me the most important thing is the camp, is the games. The priority is to get out of the Nations League," he added when asked about his desire to take the role on full-time.
"That's a big thing and just doing a good job. Don't really worry too much about the future."
Squad in full:
Goalkeepers: Jordan Pickford (Everton), Nick Pope (Newcastle), Dean Henderson (Crystal Palace)
Defenders: John Stones, Rico Lewis (both Manchester City), Harry Maguire (Manchester United), Marc Guehi (Crystal Palace), Ezri Konsa (Aston Villa), Levi Colwill (Chelsea), Tino Livramento (Newcastle), Trent Alexander-Arnold (Liverpool)
Midfielders: Declan Rice (Arsenal), Kobbie Mainoo (Manchester United), Conor Gallagher (Atletico Madrid/ESP), Angel Gomes (Lille/FRA), Phil Foden (Manchester City), Morgan Gibbs-White (Nottingham Forest), Cole Palmer (Chelsea)
Forwards: Harry Kane (Bayern Munich/GER), Ollie Watkins (Aston Villa), Jarrod Bowen (West Ham), Bukayo Saka (Arsenal), Anthony Gordon (Newcastle), Jack Grealish (Manchester City), Eberechi Eze (Crystal Palace), Noni Madueke (Chelsea)
