West Ham United fans vented their fury at Sam Allardyce during their team's 6-0 hammering at Manchester City – by singing obscene chants inviting him to leave his job.

While Allardyce accepted that the invective was understandable given the terrible Capital One Cup semi-final first-leg result, the 59-year-old risked angering supporters further by suggesting the margin of loss was as good as West Ham might have expected.

On a night when the ease of the defeat meant Edin Dzeko, who scored twice, mistakenly thought City had won 5-0, Allardyce said: "What do you expect when you've got lads on free transfers playing against players that have cost hundreds and hundreds of millions of pounds? You can do better than we did, but we'd need a fully fit squad. I had a left-back playing centre-half that we got on a free transfer [George McCartney] and that's not fair on him really, having to play against [Alvaro] Negredo and Dzeko.

"We got [on-loan Wolves defender] Roger Johnson in and I thought he did OK, even though we lost 6-0. It's not a good time for us to lose 6-0 but it's not like they haven't done it to anyone else. They've done Manchester United [4-1], done Tottenham [6-0], Arsenal [6-3], and we have to face the fact that they're miles better than us."

Regarding the obscene chants aimed at him, Allardyce said: "It is life, isn't it? When you are not doing well you get stick as a manager – and I am getting stick at the moment – that is the way it goes, that is the way this job is. You take it on the chin and get on with it. You can understand, when they travel all this way and the team gets beaten heavily, that they are going to give you some criticism. But we are not the first team to get beat here by many goals and we won't be the last."

West Ham are second-bottom in the Premier League and Allardyce admitted that, as he takes the team to Cardiff City on Saturday, the side must turn the form around or his job is in danger.

"You cannot keep losing football matches, that is for sure as a manager," he said. "You cannot think it will be allowed to continue. I don't want it to continue. We know the reasons why, but in the end even those reasons won't save you. We have got to not lose confidence in our own ability and get out of this hole we are in at the moment. We have to get ready for Cardiff and dig ourselves out of the bottom end of the Premier League by getting the injured players back and being successful in the market pretty quickly."

Dzeko had indicated how easy it had been for City when getting the final score wrong. "We are getting better all the time. It's not easy to win 5-0 at home against a Premier League team but we did," he said. Then, when told of the correct result, the striker said: "Was it 6-0? Oh."

His manager, Manuel Pellegrini, saw the funny side of the situation. "That happens sometimes. I don't know why it was a mistake for Edin Dzeko but it doesn't matter if we score one goal more or less, I think it is very important the way the team played today," he said.

With Negredo scoring a fine hat-trick and Yaya Touré adding a single goal to complement Dzeko's two, City are all but through to a final against Manchester United or Sunderland at Wembley on 2 March.