Goals from Mauro Zarate, Stewart Downing and Carlton Cole gifted the Hammers their first win of the season, following last week’s heart-breaking defeat to Tottenham Hotspur.
After their clinical display at Selhurst Park, Allardyce was full of praise for his players and says their performance has mended the wounds of their defeat to Spurs.
"I think that tactically we were outstanding today. Within those tactics the players have to play well and they certainly did," Allardyce told Sky Sports.
"Last week we didn't have the cutting edge, but our finishing was of outstanding quality this week. If we had one of those quality finishes last week, then we’d probably have six points.
"It's a fantastic performance as well as a fantastic result for us, and three very good goals have seen Crystal Palace off."
The Irons boss reserved special praise for forward Zarate, who broke the deadlock in the first-half with a sweetly-struck volley to leave Palace keeper Julian Speroni with no chance.
"Zarate has the cutting edge, he's also got the clever brain in where to find the little spaces you need to find when Palace play with two banks of four," Allardyce said.
"He dribbles into those areas and the finish was exquisite today. He's an accomplished player on the ball for us – he holds it up very well and brings other players into the game which surprised me.
"We knew he was a goalscorer but a lot of his possession was very good today."
Having only won four times away from home last season, Allardyce was delighted to secure all three points against a managerless Palace and hopes that it will be a sign of things to come for his side.
"Let's hope it’s a record-breaking away adventure for us this year and of course make sure that when we get back home, we get some results," he said.
"Today, everything was perfect. The performance, the way the lads played and how they applied themselves."