The Hammers, who will face either Birmingham or Blackpool on May 19, are 90 minutes from an immediate return to the Premier League after completing a 5-0 aggregate demolition of Cardiff.
"It's a big pressure for us and whoever we get we will probably be favourites again," said the Hammers boss.
Goals from Kevin Nolan, Ricardo Vaz Te and Nicky Maynard ensured their were no jitters at Upton Park following their 2-0 first-leg win in Wales last week.
Allardyce added: "But what a fantastic stage to go and play on. Hopefully the players can deliver yet another outstanding performance.
"The away game gave us the platform and this performance, to top it, was terrific. I'm pleased for all the players, the staff and the fans. We've got a massive opportunity over 90 minutes to get back into the golden league, where it all happens."
Nolan got the ball rolling with the crucial first goal, nodding in the rebound after Carlton Cole's header was blocked on the line. The Hammers' 13-goal captain said: "The goal settled us down, but I thought over the two ties we were the better side. Now we'll look forward to Wednesday night and finding out who our opposition is."
West Ham doubled the lead, and ended any lingering hopes of a Cardiff revival, five minutes before the interval when Vaz Te skipped behind Stephen McPhail and rifled the ball across David Marshall. And substitute Maynard had the final say with a superb finish from Henri Lansbury's through-ball a minute from time.
The only down side was the shoulder injury suffered by Jack Collison, the two-goal hero from the first leg, although Allardyce said: "I wouldn't rule him out of the final straight away."
As for Cardiff, they began the season with victory at Upton Park but ended it suffering play-off heartache for the third successive year.
It could have been different had referee Mike Dean not waved away an early penalty claim when Winston Reid sent Kenny Miller tumbling to the floor.
"I've not seen it again, but little things change games," manager Malky Mackay said.
"But West Ham were clinical. We're obviously disappointed, but we knew it would be a tough task.
"Congratulations to West Ham, they deservedly got to the final and good luck to them."
- Related links