A pair of second-half penalties from Matt Taylor and Jack Collison ensured the Hammers booked a quarter-final spot in the Capital One Cup with a 2-0 win over Sky Bet Championship leaders Burnley at Turf Moor.
It was a much-changed West Ham side, with Pelly Ruddock making his debut and teenage wing-backs Daniel Potts and Leo Chambers also coming in, yet Allardyce was once again left crowing about another shut-out on their travels.
Robbie Brady's penalty for Hull at the KC Stadium remains the only goal the Hammers have conceded in half a dozen away games this season, although half of those contests have ended in 0-0 draws.
Their profligacy in front of goal remains a concern for Allardyce, who is also keen to improve on the solitary clean-sheet they have registered at home in that time.
"When you look at our away record now, even with the team I've picked (against Burnley), we've conceded one penalty that wasn't a penalty at Hull City," said the Hammers boss.
"That's the backbone of our fantastic away performances this season which haven't really brought us enough wins.
"It's a fantastic record to keep hold of and what we need to do now is turn our home performances into results and we'll be all right."
Allardyce admitted that it took the introductions of Collison, Stewart Downing and Kevin Nolan to see them past a Burnley side which had won each of their last 10 games in the League Cup at Turf Moor.
Yet, with their development squad currently topping the Barclays U21 Premier League table, Allardyce suggested he is keen to continue to utilise West Ham's next generation in the Capital One Cup.
Allardyce added: "When I have a team of youngsters in the under-21s and my coach comes in week on week and marks them down and gives me a report saying seven, eight, nine, nine, eight, eight, nine and they're top of the under-21 league, winning every week, I have to do something about it. I have to give them a chance."
Victory for West Ham saw the Clarets' streak of eight successive wins curtailed as they tasted defeat for the first time since August.
"Make no mistake there was a lot of positive things," said boss Sean Dyche on the day he celebrates a year at the Turf Moor helm.
"Their squad is £50-odd million's worth so to play like we did against that is fantastic, great signs of what we're trying to achieve here. We had four changes as well, that's invaluable pitch-time for some of those players.
"It allows those players who had knocks and the ones who had minor strains (to rest) and we're hopeful they'll be back for the weekend. So, some really good signs again but we come away disappointed because I like winning, simple as that!"