The Hammers made their way into 10th place on Saturday on the back of a 2-0 victory over Wigan Athletic.
Allardyce's side have found form at just the right time, with a five-match unbeaten run taking them through the 40-point barrier and ending any lingering relegation fears.
The target now is to maintain those standards and end the campaign inside the top 10.
Allardyce told Sky Sports: "Very pleased, and tenth in the Premier League. It's our first season back in the big league and if we can finish around this position, this was our maximum finish for us this season. We felt that our absolute maximum would be around tenth, if we could get there.
"We have had a really good run, I think in the last 10 games we have lost only three of those 10, won four and drawn three.
"We have put a really good stint in at the end of the season after a difficult time with all the injuries we had in December. We have really stepped up to the mark again and we have done a clinical job today, a professional job.
"We made life very difficult for Wigan, even with all the possession they had to create open and clear cut chances. At the other end, we showed that we have become more clinical in our finishing over the last few weeks, and that's why we are picking up wins instead of the losses through December.
"The clinical finishing today - Matt Jarvis' cross-cum-goal and Kevin Nolan's finish for his 100th goal - edged us just ahead of Wigan and got us a very valuable three points to take us to 42.
"I know mathematically we are still not safe and people will say I shouldn't say this, but it's been a long, long time since someone went down with 42 points."