The 58-year-old replaced Avram Grant at the Upton Park helm following the club's relegation from the top flight in the summer of 2011.
Allardyce confounded the critics to take West Ham up at the first attempt via the play-offs and the club now sits 14th in the Barclays Premier League.
However, the former Bolton manager's contract is up at the end of the season and negotiations on a new deal are not expected to get underway until survival is secure.
Cole, who re-joined the club from Liverpool in January, believes that target is not far away and hopes Allardyce is rewarded with a new deal.
"Sam has done a great job and has been fantastic with me," said the 31-year-old midfielder.
"He has an unbelievable record as a manager, is an experienced manager and you see what he is about on a daily basis. What a great manager he is.
"We want to stick another two or three wins on the board and I am sure that will be much more than enough (to secure survival).
"The gaffer came in when the club was in a bad state and has done a phenomenal job.
"The owners have done a great job backing him and the lads, the players, have done a great job to come up. It is very difficult to do that.
"We can't rest on our laurels now. We've got to constantly move forward and try to win every game."
There is also forward momentum off the field, with West Ham's move to Olympic Stadium confirmed on Friday.
The Hammers have been handed the keys to the London 2012 centrepiece after completing long and tortuous negotiations with the London Legacy Development Corporation.
The agreement sees West Ham become anchor tenants under a 99-year lease, with the stadium now to be transformed into a 54,000-seater venue in time for the 2016-17 season.
For Cole, back at the Hammers 14 years after making his senior debut, it is an exciting time.
"It is a massive moment for the club,- probably one of the most significant in the club's history," he said.
"It gives the club a chance to compete at the top. The great thing is you have owners with the club at heart and want to do the right things for the club. It is a fantastic day and gives us a right chance in a few years.
"It is up to us build now and keep building. Football is not just about the team on the pitch now, it is about the team off the pitch right from the owners all the way through to the person making cups of tea at the stadium.
"It is a business as well as a football club and it is so important to the community. I am just so pleased and I am glad it is done.
"For me, it is a no brainer. It is a long-term deal and brings money, jobs and community inspiration to the area.
"It is a win-win deal and you don't get many of them."
But while many are excited, the move has provoked criticism from some West Ham supporters.
"I understand some of the fans might by wary," Cole added. "Upton Park is home but times have to move on.
"There is enough rich history at this club that we could go and play in Timbuktu as long as the fans are there and turn up.
"People won't be forgotten and historically this is one of the biggest clubs in the country so it is going to a great start for the club."
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