West Ham have exceeded expectations so far this season, sitting seventh in the Premier League to put themselves firmly in the hunt for a place in Europe.
The London club also came out on top in a thrilling FA Cup third-round replay against Everton, with goalkeeper Adrian holding his nerve to score the winning penalty in a 9-8 shootout victory at Upton Park.
Allardyce's men now turn their attention to facing League One promotion-hopefuls Bristol City in front of a sell-out crowd at Ashton Gate, when they will be out to avoid a second shock defeat of the season at the hands of a third-tier side.
Sheffield United beat West Ham on penalties in a League Cup tie at Upton Park back in August and Allardyce believes that should serve as a reminder that they should not expect to have things all their own way.
He said: "It'll be an extremely difficult game, it always is against lower league opposition, especially away from home.
"We lost to Sheffield United earlier in the season on penalties, at home in the Capital One Cup so we know how difficult it is.
"Tottenham found it difficult against them [Sheffield United] too [in the League Cup semi-final first leg], as did Liverpool against Wimbledon, but for the brilliance of Steven Gerrard they may have struggled.
"It's all down to the attitude of the players. If they take anything lightly then they can get caught cold. Starting on the front foot has always been important in these types of games."
Steve Cotterill's Bristol City side are second in League One and head into the game on the back of a four-match winning run.
"Outside of our dressing room, the pressure is off," said Cotterill. "We have to have a certain amount of belief in ourselves because otherwise we may as well not turn up.
"We know we have to play to our maximum and potentially they have to have an off-day. We may need a little bit of luck, we know that, but these things can happen in the FA Cup.
"We won't be shouting from the rooftops to anyone this week. We're very grounded and if we can maintain that between now and the end of the season, given the relative success we've had so far, that'll be great."
Allardyce stated his intention to field a strong side, with only James Collins and Diafra Sakho sidelined due to back injuries.
Cotterill has injury concerns over strike duo Aaron Wilbraham (hip) and Kieran Agard (ankle), while James Tavernier is cup-tied. On-loan duo Matt Smith and George Saville are available for selection.
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