Former Sheffield United striker Hulse, who angered the home support and players in the 13th minute when he flattened goalkeeper Lee Grant with a late challenge for which he was booked, struck in first-half stoppage-time.
Hulse headed home Gary Teale's left-wing free-kick from eight yards out to end a five-game winless run for Nigel Clough's side.
Derby are now eight points above the drop zone and have two games in hand over many of the sides below them.
"Psychologically it is definitely a big boost to get over the 50-point mark," said Crosby.
'Obviously we are not safe but it is good to get over that barrier.
"We aren't setting ourselves any targets as far as points go, just to get to a point where we mathematically can't go down."
Crosby admitted the timing of the goal could not have been better and reserved extra praise for matchwinner Hulse.
He said: "It was a good time to score but the first goal, whenever it comes, is always important psychologically and on the stroke of half-time the lads came in buoyed.
"Hulse did superbly. He is a lad who is obviously not physically right. He has got quite a lot of strains and pulls and he has got a stomach problem but he has been fantastic and he gives his all every time he goes out.
"He's got a fantastic goal and I'm sure he enjoyed coming here and scoring. It was a magnificent ball in and a great header."
Brian Laws also lamented the timing of the goal, which the Wednesday boss conceded could not have come at a worse time for his side.
Laws also slammed his side's defending for the goal, which leaves the Owls with only five points from their last seven home matches.
"I'm probably as frustrated as the supporters are because this has come on the back of a good win at Norwich," said Laws.
"We didn't play the football we have been playing in the first half and then it was a sucker punch at half-time, which is when you least want that to happen because it changes my team talk immediately.
"I had certain thoughts prior to that goal and it totally turned it around.
"If you look at the way we conceded, they had three in the box and we had five.
"Maths tells you there shouldn't be any space for them but Hulse got a free header and I am disappointed with our defending and I let them know at half-time."
The Wednesday manager at least took heart from his side's second-half display.
Laws added: "We were much better after the break and we put Derby under pressure and had enough chances to get the result.
"Derby had a bit of fortune, we hit the crossbar and had balls cleared off the line and Marcus Tudgay has had three opportunities, but that sometimes happens."