The Eagles supremo says he is aware the club need to strengthen in the January transfer window and he's in talks with American investors Josh Harris and David Blitzer about how much money there is to spend.
With Palace just one place and one point above the relegation zone, the squad Allardyce inherited appears in need of freshening up and Parish is working hard on deals.
"Maybe this break from the league now helps us. It also helps us to try and work on a few players and we're going to stay calm while we're doing it," he told Holmesdale Radio.
"The good news is that we're not in the bottom three, we have got winnable games and a decent squad. The bad news is that we're low on confidence and we're lacking in a few areas, so we need to try and fix that.
"I've spoken to Josh and David, in the context of not splurging money and doing what we want. We're moving heaven and earth to do the things we need to do to support the manager and support the team."
Palace are believed to be keen on Arsenal defender Carl Jenkinson while Swansea winger Modou Barrow has also been linked with a move to Selhurst Park recently.
Parish says he expects to sign at least one player before the club's Premier League campaign resumes against West Ham on January 14 following the FA Cup third-round clash at Bolton on Saturday.
He added: "I would be really disappointed if we didn't have something in place for West Ham. That's got to be the aim, hasn't it? Everybody needs a lift and we all recognise that, but we're not going to be taken advantage of. We have got the long-term future of the club at stake. We're trying to do the best deals we can with the time available.
"Sam Allardyce is working tirelessly on it, watching videos and looking at opportunities. I am working on two or three that we think are real possibilities.
"People have got to remember the player needs to be available. You can also waste your time on the overseas transfers, too. So we are doing our best, we're not doing anything else other than that, morning, noon and night. There is not a lot of sleep going around at the moment.
"We want to bring in more than just one player, so we need to do what we can. It's not just as simple as overpaying either, because if we overpay then it reduces what we can do on other things."
Crystal Palace last week