The Hammers were still in the contest at half-time with Charlie Austin's 40th-minute goal separating the two sides at break at the London Stadium.
Having conceded four goals in each of their last two Premier League matches, West Ham were intent on defending stoutly for once but Bilic admits that after a number of poor results of late, the idea was to get at the Saints in the second half in a bid to arrest their run of defeats.
"They deserved it. We started well, with people behind the ball and closing the opponent down. We were defending well as a team, considering we had conceded eight goals in the last couple of games," he said in the wake of a fourth straight league loss and seventh in 11 matches in all competitions this term.
"In the first half, in that part of the game we were good, we were compact and everything. But we weren't happy with the way we were with the ball, especially in the last third of the pitch, where we didn't penetrate enough.
"The first mission was to be better defensively, but that should be the mission in every game. In the first half we were solid and regrouped well behind the ball, but we're at home and need points and we were not happy with the way we attacked when we had the ball.
"We were a little bit unlucky in the first half, because they didn't deserve to be one up in my opinion.
"In the second half we were trying to get back in the game, but we made one big mistake and they took advantage of it.
"After it went to 2-0, we tried to put them under pressure and had a couple of chances which were on target, but they were always very quick in the moment of transition and had a few chances as well."