Despite an early goal from Martin Devaney, Tranmere suffered a 2-1 defeat to Bournemouth on Saturday afternoon.
The winger netted his second goal for the Club in the opening minutes of the game but the combination of a deflection and a cross put the home side ahead after half an hour.
Rovers battled for an equaliser but they were unable to find a way past Darryl Flahavan a second time.
There were two changes to the side that started the goalless draw against Rochdale, as James Wallace made his debut in midfield in place of Ash Taylor and Mustafa Tiryaki recovered from illness to take the place of Lucas Akins in attack. Joss Labadie missed out with a foot injury while Rovers were still without Owain Fon Williams, Andy Robinson, Dave Raven, Zoumana Bakayogo, Adam McGurk
&nbsp;and Enoch Showunmi.
Wes Fogden send the game's first shot wide of Paul Rachubka's near post in the second minute while Rovers responded swiftly with Tiryaki forcing Darryl Flahavan into a decent save.
The shot earned Tranmere a corner which was followed by two more in quick succession. However, from the final set piece a miss hit by Robbie Weir allowed the hosts to launch a counter attack from which Wes Thomas shot wide.
The action swung back to the Bournemouth end on four minutes when Tranmere took the lead. Rachubka's long clearance took a touch off the head of Stephane Zubar and Martin Devaney reacted fastest to send his shot from outside the area past Flahavan and into the net.
Rovers had the chance to double their lead on 16 minutes when David Buchanan broke into the Bournemouth area and played the ball towards Weir. However, after the midfielder missed his shot the ball fell to Wallace who shot wide of the target.
Two minutes later the Cherries drew level. Michael Symes and Thomas combined with the latter's shot taking a deflection, looping over Rachubka and into the Rovers goal.
Wallace sent a shot on the turn over the bar on 28 minutes but two minutes later Rovers found themselves trailing. The home side took a short corner from which Pugh's cross went past everyone into the area and into the Tranmere net.
Pugh sent a header over the bar from Charlie Daniels' cross on 32 minutes and three minutes later Harry Arter fired high over the bar from long range.
A late cross from Devaney was cut out of the path of Tiryaki as he went in search of an equaliser before half time.
Elford-Alliyu was replaced by Akins for the start of the second half and the striker's long throw earned Wallace a long range shooting opportunity early in the period though his effort went wide of goal.
John Welsh sent a volley over the bar on 52 minutes and an Akins shot on the turn was saved by Flahavan three minutes later.
Rachubka comfortably held Arter's effort from outside the area on 57 minutes while another attempt from Akins was kept out by Flahavan following a deflection.
Goodison did well to deny Thomas a shooting opportunity on 68 minutes and the Jamaican almost got on the end of a Tiryaki free kick seven minutes later.
Goodison moved into attack in the final ten minutes, a change that also saw Ash Taylor come on for Weir.
However, Rovers were unable to create a clear opening and went home empty handed.
Bournemouth: Flahavan, Francis, Zubar, Cook, Daniels, Fogden, Purches (Gergory 82), Arter (MacDonald 64), Pugh, Symes (Fletcher 82), Thomas. Substitutes: Jalal, Cummings.
Tranmere: Rachubka, Holmes, Goodison, McChrystal, Buchanan, Welsh, Weir (Taylor 83), Wallace, Elford-Alliyu (Akins 45 HT), Tiryaki, Devaney. Substitutes: Coughlin, Kay, Power.
Referee: Carl Berry
Yellow cards: Wallace (43), Pugh (85)
Away attendance: 159
Follow Tranmere on Twitter at www.twitter.com/tranmererovers.