Sunderland beat Palace 1-0 at Selhurst Park, and their performance was highly impressive.
The Black Cats were defensively robust, and ruthless when they were provided an opportunity.
And Allardyce was delighted that his side cut out the individual errors which have plagued their season so far.
"It’s a big bonus for us achieving our first win away from home, and from the way we achieved it," he said.
"The lads showed they had a lot of fight in their bellies, and we’re going to need a lot of fight, grit and determination given the position we’re in.
"The best thing for me is about how few mistakes we made. We cut out the errors we have been making that cost us so many goals."
Sunderland’s tendency to make costly mistakes has seen them have one of the worst defensive records in the Premier League, but they have shown signs of improvements recently.
The Black Cats were only beaten 1-0 by Southampton in their last home match, and on that day an individual error from Yann M’Vila proved costly.
Against Palace, though, the Wearsiders looked far more secure and they were rarely threatened by Alan Pardew’s men throughout the contest.
Sunderland’s win over Palace has lifted them to within one point of safety, with their next match coming against Stoke City.