The Hammers booked their spot in the last four on Wednesday night after coming from behind to earn a second successive win at Tottenham this season, with Matt Jarvis and Modibo Maiga scoring in the final 10 minutes to stun managerless Spurs, who had gone ahead midway through the second half thanks to Emmanuel Adebayor.
Allardyce's side were pitted against title contenders City, with the first leg set to take place in the week commencing January 6 at the Etihad Stadium, where the Sky Blues have won all eight games in the Barclays Premier League, scoring 35 goals in the process.
"It's a tough one, isn't it? If it had been one leg and if it was a draw and it pulled out that it was at our place, not at theirs, it would have been nice," said Allardyce, whose team's only league success on their travels was a 3-0 win at Spurs, while they are hovering just above the relegation zone.
"Over two legs it makes it a little bit more difficult when you know Man City have scored on average four goals every home game."
The two Manchester clubs were kept apart, with United drawn to face Sunderland, who will host the first leg before the return clash at Old Trafford two weeks later in the week commencing January 20.
United last won this competition in the 2009/10 season and going all the way this season may go some way to easing the pressure on David Moyes, who has endured a frustrating start to his reign as Red Devils manager.
Following their 2-0 victory at Stoke on Wednesday night, the Scot admitted he is at a club accustomed to major honours, but is not looking past the Black Cats, who are struggling in the league but proved their cup credentials with a come-from-behind extra-time victory over Chelsea on Tuesday.
"We had to win the game before we got into the next round but thankfully we did and we'll have a tough semi-final against Sunderland now," Moyes told Sky Sports 1.
"It's a cup game and it shows you how well Sunderland can play when they beat Chelsea, they played well to get that result and they've got a new manager now.
"A lot of things can happen between now and then but we're just really pleased we've got ourselves into the semi-final.
"Manchester United Football Club are used to winning trophies and so it's no surprise to them. It's business as usual but I've got to say that I'm delighted that we're in the semi-final."