Second-half goals from Mark Noble, Kevin Nolan and Modibo Maiga saw the Hammers run out 4-1 winners.
“Like everybody else, I was dumbfounded by the first half and our lacklustre performance,” Allardyce told West Ham TV. “The only good thing we did was to not allow Southampton any real chances even though we weren’t playing to our best. We didn’t score a goal that would have made things easier for us and it was hugely difficult for us before half-time.
“At half-time, without me telling them, the lads knew they were under par and I just said ‘You’ve got to do the right things better and your work-rate, energy and tempo have got to be lifted by 15 or 20 per cent - not just five per cent. I told them that once that tempo was lifted and we put pressure on the opposition, they are a struggling side near bottom of the league with not a lot of confidence and they will make mistakes, which they did.
“The second goal, in particular, their left-back has been caught in possession by Yossi and he has made a brilliant ball for Kevin to score. That was the thing we were looking for and we got that right from the start of the second half. In the space of just a few minutes we were two-nil up because our attitude and desire to get forward and on the front foot and stop the opposition from doing what they wanted to do.
“They made a lot of mistakes and we went on to win comfortably four-one in the second half and, for me, it was great to see that fourth goal - not only for the quality of it but for Modibo, who has been patiently sat in the wings since he arrived in this country from Sochaux. That goal will do him the absolute world of good because it was his first goal in the Premier League. He has scored in the Capital One Cup and he has scored while he has been away on international duty and scored again today, so he’s made a big impact and that’s a great for us, especially with the injury list we have got at the moment.”