The point leaves the Owls one point and one place above third-bottom Crystal Palace, who dropped into the bottom three following Scunthorpe's victory against Plymouth Argyle.
These are worrying times for Wednesday, who have won just one of their last eight games and are facing yet another nervy end to the season.
Irvine's side had their chances against the Rams, with Tommy Miller missing a golden opportunity in the first minute.
The visitors also came close, with Lee Grant producing fine saves to deny Rob Hulse and Chris Porter.
Wednesday dominated after the break but Derby, who are just four points better off than the Owls, held firm thanks in no small part to an outstanding display from central defender Shaun Barker.
Former Preston boss Irvine set his sights on a tally of 53 points to avoid the drop when he took over in January, but he admits he may have to revise that total with eight games remaining.
He said: "We may well need four wins and a draw to get the points that we need, or that I'm hoping for."
When asked if 53 points remains his target, he added: "I still think it's going to be high, I've not really sat down and looked at it in any detail yet, but I rest easy once we get to that figure rather than being short of that.
"I do think that it will be a high total."
Irvine was left frustrated by Wednesday's finishing and has called for his side to be more ruthless in front of goal.
He added: "I feel that we desperately need some wins and this was certainly not a foregone conclusion by any means, but I think we had enough chances, and good chances, to win the game.
"Derby had their share of it in the first half, I thought second half we dominated in terms of possession and territory, had some good chances but didn't take them and that's disappointing."
Derby are also in the midst of a poor run of form, with one win in their last seven games, but boss Nigel Clough was relieved to halt a run of three consecutive away defeats.
He said: "I'm delighted with the clean sheet - we haven't kept too many recently, especially away from home.
"I'm delighted we saw the game through because we've been conceding some late goals, home and away, of late which have cost us but we saw it through today.
"I think both sides were a bit nervous. The first half was quite open but the second half they put us on the back foot for the majority of it, but we defended well.
"It was important not to lose today and keep that gap in tact.
"It's another point on the board towards the 50, 51, 52 - whatever we are going to need to stay up - and of course nine draws will do us if that's what it comes to."