The former Blackburn boss was pleased with his side's display in their 2-0 first-leg win against Cardiff City and says the onus is now on the Hammers to reach the final at Wembley
The Hammers have one foot in the Championship play-off final after a double from Jack Collison sealed a 2-0 semi-final first-leg victory in Wales.
Allardyce was happy with the performance of his players and admitted the onus is now on West Ham to see out the tie and reach the final at Wembley.
"I think that we asked the lads to control their emotions on a big night like this and not to do anything untoward that might cause us a problem for ourselves and I thought they handled the pressure very well and played very, very well indeed," he told Sky Sports.
"I thought tactically we did everything right in terms of nullifying Cardiff to minimal chances on goal in their own ground and, again, the quality on the break and getting forward was outstanding, and chances were created, scored, and a lot missed tonight.
"So it's been a great night for us but it's only 90 minutes of two-legged affair, so anything can still happen. The onus is on us now to see it through.
"No pressure on Cardiff, but [they have] to come and try and claw back anything that they possibly can, and mentally we've got to be right for that, and make sure that we go out and try and win the next game.
"But it's a fantastic night for us, and one where the players have handled the pressure extremely well, performed very, very well indeed and give us the great platform for the next leg."
Two-goal hero Collison also warned that the semi-final is not yet over and singled out team-mate Carlton Cole for praise.
"Obviously it's massive for us," the midfielder said. "We wanted to come here and keep a clean sheet, luckily we got the two goals so obviously we're in a great position now, but...we're only halfway through."
He added: "Obviously it's nice to get the goals, but it's a real team performance tonight. We all dug in really well. The defence were outstanding right the way through. Coley's [Carlton Cole] worked his socks off tonight, so it's a real good performance and we're happy."
Meanwhile, Cardiff boss Malky Mackay believes the reason for his side's loss was due to individual mistakes and bad luck.
The Scot said: "The first one [West Ham goal] was certainly poor defending from us on three points during the move. The second one is complete random luck. The ball takes a huge deflection.
"We had three or four real good chances tonight and it goes the other side of the post, or it's cleared off the line, so simple as that."