And on an Easter Saturday to forget, Hammers were almost left with egg on their faces when substitute striker Manel found the net in the final moments - only for the strike to be ruled offside, a decision that the TV cameras proved to be incorrect.
Despite the disappointment, Alan Pardew's team moved up one place into fifth thanks to a point that took them back above Millwall on goal difference but, with three play-off rivals below them all in touching distance with at least one game in hand, their position is certainly looking precarious with just five games left.
The Hammers boss had made four changes to the starting line-up following last week's disappointing 2-0 defeat his former club Reading - two of which were enforced. With Stephen Bywater's two-match suspension beginning, Pavel Srnicek came in for his full debut, but there was a huge blow in the shape of Matthew Etherington's groin injury that meant youngster Chris Cohen was also handed his first start in a Hammers shirt.
Elsewhere, Nigel Reo-Coker and Andy Melville made way as Hayden Mullins returned from a back problem to partner Christian Dailly in the centre of defence and Steve Lomas also made a welcome comeback following a season blighted by injury and illness.
The Northern Ireland international's tenacious bite in midfiel was behind many of Hammers' best moves early on as they enjoyed the lion's share of possession and created several decent chances. Bobby Zamora saw a right-foot shot blocked by Rams keeper Lee Grant, while skipper Christian Dailly sliced two efforts wide against his former club.
Cohen almost marked his full debut with a stunning goal in the 25th minute but unfortunately his blistering left-foot volley from 18 yards out flew just inches wide of the post. Moments later, David Connolly latched on to Michael Carrick's clever lofted pass and came just as close, guiding a measured volley narrowly past the upright.
Derby's first opportunity of the game arrived when Marcus Tudgay burst into the penalty area and pulled the ball back across the six-yard box, but Carrick was hand to clear and ensure that the first half ended goalless.
The young and enthusiastic Rams came out for the second half no doubt boosted by Hammers' failure to break through in the opening 45 minutes and, after Connolly was denied by a superb late tackle by French defender Mawene, it was the visitors who began to take a hold on the game.
Without creating any real clear-cut chances, George Burley's men enjoyed the better of the play and restricted the hosts to the odd long-range effort while all the time making more of an impact in the attacking third. Talented young midfielder Tom Huddlestone saw a quickly-taken free-kick kept out by Srnicek in the 58th minute, while Tudgay went close with a fierce effort that flew just inches over the bar.
Pardew attempted to revitalise his side with a double substitution in the 66th minute, introducing Brian Deane and Reo-Coker in place of Zamora and Cohen but, with the 17-year-old having provided Hammers' only real crossing threat from out wide up until then, the veteran target-man may have preferred to see his young team-mate remain on the pitch alongside him.
Jobi McAnuff then came on to replace Marlon Harewood and almost provided an instant impact when his mazy run was thwarted inside the penalty area, before Deane agonisingly missed the best chance of the game with just four minutes remaining when he somehow headed Lomas' cross over the bar from six yards out.
Rams substitute Manel then had his effort ruled out but by then many of the 28,207 crowd were out of their seats and on their way home after another lacklustre display. The majority of those who did hang on until the final whistle made their feelings clear about the performance, and Hammers will need to produce a much better display at Crystal Palace on Monday if they are to get the play-off push back on track.