Allardyce, 58, last week ended speculation about his future when he penned a new two-year contract extension after successfully keeping the east London club in the top flight.
West Ham - who plan to move into the Olympic Stadium for the start of the 2016/17 season - could secure a top-10 finish if they beat relegated Reading on Sunday.
Wales international Collins believes everything is set up for Allardyce, the former Bolton, Newcastle and Blackburn manager, to continue the club's progression.
"It is great the manager has signed his new contract, we as a team are flourishing and I know he only wants us to be getting better and better," he said.
"We are all enjoying it here. He along with all of us at the club can look to the future and plan what we want to do next in trying to take our club to the next level."
Key to West Ham staying clear of the dogfight for survival - which was ended when FA Cup winners Wigan's relegation was confirmed following their 4-1 defeat at Arsenal on Tuesday night - has been form at the Boleyn Ground.
The Irons have lost only four league games at home, in stark contrast to 12 defeats on the road.
A ninth victory at Upton Park would cement a top-10 finish and set the Irons up to press on again next term.
Collins added: "We have had a great season, to win and to finish 10th would be great.
"It is always good to finish well. In my experience if you finish one season well you normally start the next season well."
Despite their impressive return having come up via the 2012 play-offs, the Irons' tougher challenges lie ahead.
West Ham are expected to be busy over the summer, and have already been linked with moves for the likes of Celtic forward Gary Hooper and Vitesse Arnhem's Wilfried Bony - the top scorer in the Dutch league - as well as veteran Italian midfielder Massimo Ambrosini, who is out of contract at AC Milan.
Allardyce, though, accepts no matter how hard clubs might work to improve the squad, the additional financial outlay does not always correlate directly to more consistent results.
"For the small improvement, it is a considerable amount of millions which is needed today, that is the difficult we all face," Allardyce said on TalkSPORT.
"You buy a £10million player or a £12million player today and everybody expects the team to improve by 15 or 20 per cent, but often it is only by one or two per cent.
"The size of the fees for players and wages just don't relate to how much they improve the team.
"That brings more and more pressure on you as a manager in trying to improve the side.... but the money needed today is astronomical."
New Financial Fair Play rules in the Premier League next season will also impact on how much of the bumper new television income can be spent on wage bills.
Allardyce admits those changes represent uncharted water for member clubs, and last month suggested it could impact on West Ham's ability to look to make a loan move for England forward Andy Carroll into a permanent transfer.
"We have got some funds available, but the financial restrictions kick in this year and those funds will be restricted," the Irons boss said.
"We have to be careful where, and how, we spend our money to try and improve the side, which is something we must do.
"It is worrying for everybody and we will have to see how it works out. It makes life that little bit more difficult.
"But we will have to learn to deal with it and, hopefully as a team we can get better despite those restrictions."