Tony Pulis' side took four points over their four games between December 21 and a New Year's Day draw with Norwich, with the 1-1 draw on Wednesday not enough to keep Palace out of the bottom three.
An away win at Aston Villa was the highlight of the Christmas schedule, with defeats to Newcastle and Manchester City meaning Palace are still embroiled in the survival battle, but Speroni is pleased with the club's progression.
"It was very good," the Argentinian said of Palace's festive form.
"I think it was a very, very positive time for us. We managed to get some good points and build a team that is solid and get some good performances in and there is a lot to take from that."
Pulis, who has been in charge at Selhurst Park since replacing Ian Holloway in November, has said the January transfer window will be a big period for the club and Speroni has been impressed with the impact of the ex-Stoke manager.
"He has been great," Speroni added.
"The lads are starting to get to know him better and I'm sure there is more to come. The manager and chairman will sit down and see what they can do in the window but we don't know."
Speroni conceded the opening goal against the Canaries as Bradley Johnson bent in a long-range effort before Jason Puncheon equalised from the penalty spot.
The 34-year-old goalkeeper admitted the game had been earmarked as a winnable fixture but felt the poor weather conditions, with heavy rain and strong winds threatening the game before kick-off, had a big impact.
He said: "The conditions I think played a big part. It was a very tough game for both teams.
"Horrible really, horrible conditions. The ball was moving around all the time, the rain and everything. But again, it was the same for both teams.
"We wanted three points. That was the idea. We went on to the park thinking of winning the game. And sadly we couldn't. But I think we played well and there's a lot of positives to take from that."
The draw saw Chris Hughton's Norwich side slip one place to 15th in the standings and Johnson, who struck his second goal of the season to put the visitors in front, felt it was a missed opportunity for Norwich to push towards the middle of the table.
"For us personally I think we're disappointed with a draw," he said.
"I think the way the game went, we created chances, but we couldn't put them away. But at the end of it I think coming off that game we would have been very disappointed if we had lost the game. At the end of the day a draw's a draw - we haven't lost it.
"Palace is always a hard place to come and if anyone comes here and picks up points it's going to be a good result for them. I feel personally the way we played today and the way things went we deserved the three points.
"At the end of the day we'll look back at this and hopefully it will be a good point for us."