A new £5bn TV deal for the Premier League means relegated teams will receive £67m - an increase of nearly 40% - stretched over four years to help soften the blow.
New Financial Fair Play rules imposing wage restraints and club losses in the top flight aiming to provide a more 'level playing field' also offers hope for those managing lower league clubs.
Poyet, though, is sceptical about the inflated hand-outs. Having been at the helm at Championship side Brighton since 2009 and currently pushing for promotion, he told the Footballers' Football Show: "Parachute payments help and it means you still have the best players, you have extra money to spend and there's the financial fair play rules coming in.
"But if the clubs don't produce money or if they are not very smart attracting companies, sponsors and people to the stadium it will be very difficult for these teams to compete.
"It's going to be massive. If teams don't go back up straight away there will be a group of 10 teams that will be very strong financially. For the rest, if they go by the rules I think they will struggle.
"The Premier League is the best league in the world and I don't know if the payments are fair or not, but it makes it more difficult for the rest. The three teams that came down last season - Wolves, Blackburn and Bolton - they haven't been in the top six [in the Championship].
"I won't get involved in what the boards have decided in those clubs with the change of managers but it looks like those decisions didn't work for those teams."
Aidy Boothroyd, currently managing Northampton Town, enjoyed steering Watford up to the Premier League in 2006, only to suffer the drop the following season and was axed in 2008.
Boothroyd, also sacked by Coventry in 2011, agreed the hand-outs were helpful but echoed Poyet's sentiment that clubs - and players - needed to be managed carefully to ensure long-term stability.
"It is a gamble to survive in the Premier League," the 42-year-old told the Footballers' Football Show.
"It's all relative to the club you're in. When you get into the Premier League and you get that money, you think you've cracked it. It only takes two weeks to realise you're nowhere near everybody else!
"And then when you come down, you get a lot of other problems. Many of the players have been paid more and they have to take cuts and that's how it should be, but the issue is they think they should still be in the Premier League.
"That causes a range of motivational issues and there's this talk of a relegation hangover. Often those teams bounce back into the Premier League.
"When we (Watford) were in the Premier League we found that we started brilliantly. We had a blip and it just got bigger and bigger and you also face teams that are much hungrier.
"You then get into a situation where you need to change players quickly or change managers and that's what generally happens first and that's what happened to me."