The Blues are looking for their first back-to-back away wins since September 2016 but face a tough test against Carlos Carvalhal’s resurgent Swans.
Speaking to the media at Finch Farm, Allardyce said: “We need to be at our best, not be complacent.
“The players cannot slip from the levels they need to get against a team like Swansea that are fighting relegation. You’re meeting a team head-on on Saturday who are needing points to avoid the drop and their crowd come to get behind them.”
“We have to try and put together a performance like we did at Stoke last time we were away. We’ve got to get a result,” Allardyce continued.
“Our home form and home performances has been fantastic and we’ve just got to maintain away results now.”
The Everton boss was also quizzed on the fallout of Wayne Rooney’s reaction to being subbed during last week’s Merseyside Derby.
Rooney was seen to be visibly annoyed and frustrated at being subbed off and his exit from the game was also met with dismay from parts of the Goodison Park crowd - with some booing the decision.
Allardyce said: “A reaction from a player when he comes off of disappointment is to be expected. A man, as proud of being an Everton fan as he is and playing for Everton, that’s where the reaction came from.”
“We speak every week,” Allardyce added and followed with a laugh. “We’re alright, not a problem.”
“There’s no problem with Yannick Bolasie and no problem with Tom Davies and no problem with Wayne Rooney. All three of those players were substituted last weekend.”
He added: “We’ve said many times, it’s a role he wants to play and our tactical change was for the benefit of the team on Saturday.
“It’s a team game and you make a decision on the day to try and help the team get a victory and we did with three substitutions - and played a game at the end of the derby by pressing Liverpool for the last 20 minutes.”
The Blues will have a relatively full bill of health for their trip to South Wales, with only a number of long-term injuries out and unavailable.
Idrissa Gana Gueye, who had been expected to start last weekend, was a late change after a late injury reaction to his hamstring. He’ll be fit and ready for the trip to face the Swans.
However, Gylfi Sigurdsson is going to be “touch and go” on whether or not he plays before the end of the season.
The Blues have had hopes he would play at least once more before the close of the campaign in a bid to boost his fitness prior to the start of the World Cup.