"It's a massive turnaround for us all," Allardyce, fondly known as the 'Big Sam', told West Ham TV after Tuesday's 2-0 victory over fellow strugglers Norwich City lifted them up to 10th in the table.
"This was a really hard fought game between two teams going at it head-to-head, both wanting to win to try and ease that pressure on them being close to the bottom."
Allardyce has yet to suffer relegation as a manager and is known for putting defensive stability ahead of expansive football and though the team's style may not be easy on the eye, it has been effective in recent matches.
The goalless draw at Chelsea was ugly and attritional, with the three wins since achieved by a combination of stout defending and making the most of the few chances they have created at the other end.
Their performance against Chelsea invited manager Jose Mourinho's wrath, who claimed that Allardyce's West Ham played "19th century football" and had no intention of settling for anything more than a draw.
Not that Allardyce will be at all concerned with the criticism after the Hammers extended their run of not conceding a goal to four matches following their 13th clean sheet, the most in the league this season.
CLEAN SHEET
Their third straight win came courtesy of two late goals, with James Collins rising to grab the lead after 84 minutes while Mohamed Diame secured all three points with a counter-attacking goal in injury time.
"It was a really hard-earned victory for us and another magnificent clean sheet," Allardyce said.
"To get that clean sheet, our goalkeeper Adrian made three outstanding saves, which he hadn't had to do recently because he hasn't been stretched in terms of making those type of saves.
"He made them at critical times for us and that gave us the opportunity to get the win.
"When you win as late as we did, it sends everybody home happy and relieved and very grateful that we've got another three points."
With just four points separating West Ham from the relegation zone, Allardyce is aware that a last-minute scrap for survival still remains a possibility with 12 games remaining.
"Tenth in the league now, but it doesn't mean an awful lot because there aren't many points between 10th and third from bottom, so hopefully we'll continue onwards and upwards with Southampton in 10 or 11 days time," he said.
West Ham are without a fixture this weekend as the league makes way for the fifth round of the FA Cup, a competition the Hammers are no longer involved in this season.
(Writing by Sudipto Ganguly; Editing by John O'Brien)
