Allardyce delighted with away win
The club's sixth win in their last nine Premier League matches was sealed thanks to goals from Andy Carroll and Mohamed Diame on Monday.
Adam Johnson's 65th-minute strike ensured a nervy ending for the visitors, but they stood firm.
Sunderland remain deep in relegation danger but Allardyce feels his side are now essentially safe - something that was far from a certainty earlier this year.
"It's a fantastic result for us," Allardyce told Sky Sports.
"It's going to be very difficult for the bottom three sides to catch us now.
"Every game in the Barclays Premier League is a tough one, every away game particularly. I thought the lads handled it really well.
"It got a little nerve-wracking towards the end when they got the goal. I think it was a really good finish from Johnson.
"Andy Carroll, particularly in the early stages, really settled us down and then Mo Diame … really made life difficult for Sunderland (with his goal).
"(It is) a fantastic win at this stage of the season for us."
Allardyce was quick to sing the praises of Carroll, who deservedly won the man-of-the-match award for a typically powerful display.
"Andy gives you an alternative. As a player, he is unique in many ways," he added.
"There's not too many who can receive a ball or head a ball as good as he does. You saw the headed goal from the corner - there was nobody going to stop him.
"(And) there's a lot more about him on the deck than people gave him credit for."
West Ham captain Kevin Nolan rejected claims he was lucky not to concede a penalty when he elbowed a loose ball during the first half and was proud of his side's ability to adapt to a game plan.
"I said at half-time that it's definitely not a penalty," Nolan said.
"I haven't thrown my arm up. I would have been devastated if it was a penalty.
"We knew obviously it was going to be tough tonight. I thought we dealt with them well. We came here with a game plan, the game plan worked a treat and we take the three points."
Goalscorer Carroll - who came through the ranks at Sunderland's arch-rivals Newcastle United - said his goal was extra special given the opponents.
"Scoring against Sunderland is a great feeling," Carroll said.
"But three points is more important."