The Hammers are turning around early-season form as they seek to remain in the top flight.
A 2-0 win at home to Norwich on Tuesday night made it three consecutive wins - a feat not achieved by the club since the 2006/07 season.
"It is just delightful," Allardyce said.
"An outstanding victory and a hard-earned win - 13 points from six games is a terrific run of form considering where we were and the trouble we were in.
"Even 10th might not be out of trouble - we have to continue and get more results.
"It's a great end to an important run of fixtures. If Norwich continue like that, they will have no problems. They were very good and gave us a good game."
Allardyce was again left singling out the heroics of goalkeeper Adrian, who kept his fourth clean sheet in succession to set his side up for another valuable three points.
"Our goalkeeper kept us in the game," Allardyce said.
"We scored late, when it is hard for anybody to come back into it - his reward was us winning it."
- Sports & Recreation