The Premier League’s bottom club suffered more misery against Championship opposition with Josh Brownhill’s 72nd-minute strike proving the difference between the two sides.
“We have lost the last nine games in a row and seven of them have been by one goal,” lamented Town chief Wagner.
“It’s tough to pick the players up and it’s the same for everyone at the football club.
“We are in a difficult period and I didn’t see it coming, but we have to get through it.”
Asked if he felt under pressure, Wagner replied: “To be honest, I’m not the right person to get asked this question, which is why I can’t answer it.
“The fact is the responsibility is mine for what has happened at the football club in the last three-and-a-half years, and that includes what’s happening at the moment.”
Huddersfield owner and chairman Dean Hoyle has declared he has no intention of letting the club “sleepwalk into relegation” and it is clear that Wagner needs help in the transfer window.
The Terriers are eight points from league safety – the 17th position occupied by their next opponents Cardiff – and have only scored five times in their last nine outings.
“I’ve no idea,” said Wagner, who has been linked with Sunderland striker Josh Maja, about the possibility of signing a forward this month. “Everybody knows the circumstances we have at our football club and that financially we are not at the top.
“We will just have to see what we can make happen. The focus was always on Premier League survival before (Bristol City) and Cardiff is obviously a big game.
“We have to get the feeling back that we are able to win football matches and collect points.
“That’s why the Cardiff game is so big for us – not because it’s Cardiff and we have an eight-point gap to them. But because it’s our next game and we have to get the winning feeling back.”
Bristol City’s win took them into the fourth round of the competition for only the third time in 12 seasons.
Bristol City: Maenpaa, Hunt, Wright, Webster, Dasilva, Eliasson, Brownhill, Morrell, Paterson, O’Dowda, Diedhiou. Unused substitutes: Taylor, Weimann, Kelly, Kalas, O’Leary, Eisa, Pearson.
Huddersfield Town: Hamer, Durm, Jorgensen, Stankovic, Lowe, Bacuna, Hogg, Kachunga, Puncheon, Diakhaby, Depoitre. Unused substitutes: Lossl, Kongolo, Billing, Mbenza, Pritchard, Mounie, Hadergjonaj.
Referee: P Bankes (Merseyside).