West Ham started their season with a hard-fought win over Aston Villa last weekend while their opponents on Saturday opened up with an impressive 5-0 hammering of QPR at Loftus Road.
And while Allardyce was happy to collect three points, he is wary of the momentum the Swans have following their rout at Loftus Road.
He said: "We didn't quite hit the heights Michael (Swansea manager Michael Laudrup) did, but we had a 1-0 win against Aston Villa, which was a fantastic result for us.
"But the dizzy heights Swansea achieved at QPR on Saturday was a dream come true for Swansea and for Michael.
"Listening to the facts, I think it was January before they won their first away game in the Premier League last season. So to start the season away from home and to win the game, and win it 5-0, Michael must be delighted.
"It gives them a lot of confidence going into what has already been a fantastic home record in the Premier League last season.
"Their home record was exceptionally good so, as every game, it will be very tough and perhaps a bit tougher because they have that confidence of winning the first game 5-0."