The Hammers boss was delighted with the 24-year-old's equaliser that salvaged a "precious" point on the road, while Mauricio Pochettino insisted his Southampton side deserved more
The Liverpool striker made the temporary move to Upton Park in the summer after Brendan Rodgers took the helm at Anfield, but he failed to make an instant impact after suffering a number of injuries.
However, the 24-year-old has now netted five times in seven appearances, including the goal that earned the Hammers a vital point against Southampton on Saturday, with his boss suggesting his ability has never been in doubt.
"It's marvellous, we've been waiting for it and I told you it would come," he told reporters. "When we got him match fit I said he would bring the goals and Andy's fully match fit now and took his goal very well off the free kick.
"He should have had another one in the six-yard box just after half time [when] he put it wide of the post, and he knows that should have been a goal but at least he made up for it and got us a precious point."
The east London outfit came from behind to secure the draw against a side that had won their previous three matches, and the former Blackburn manager was delighted with the result.
"If you come back from 1-0 down you would be happy with a point away from home," he continued. "I did feel we had the better chances to go 1-0 up though.
"Considering they've beaten Liverpool and Chelsea in their last two home games we've nullified their attacking points very well today, creating our own chances and thoroughly deserved the point."
Allardyce's men now sit on 38 points, which the Englishman believes should be enough to see them remain in the Premier League next season.
He added: "Everybody will say we're not mathematically safe, which is true, but it's highly unlikely that we won't pick any more points up before the end of the season.
"I would hope we will continue our home form and pick up points in our next two games to make sure we are really safe, and then push on from there."
Saints manager Mauricio Pochettino, on the other hand, felt his team deserved all three points from the uninspiring clash at St Mary's, and lamented his players inability to hold on to the lead.
"It was a hard-earned point, but it wasn't enough of a consolation for the performance my players put in," he argued via his translator.
"When [Gaston] Ramirez scored the team was playing really well. We deserved to be winning judging on how we played in the first half and part of the second as well.
"It's just a shame we conceded that goal really quickly after we scored. At the end of the match we had some good chances to win it, they did as well, but overall this point doesn't feel good enough. We feel like we should have won the game."