The Hammers were beaten 1-0 by Ronald Koeman’s side on Saturday, after falling behind through an early goal from Maya Yoshida.
And Bilic believes his side gave Southampton a headstart, as they kept giving their hosts needless set pieces.
"It was one of those defeats that is really hard to take and it was down to – I said this to the guys in the dressing room at half-time – the first 15 minutes,” the Croatian boss said.
“We basically gave them a couple of corners unnecessarily, they were better on the second balls, they were better in the first 15 minutes.
"We started better in the second half and then when they were with 10 men we were dominating and all that but we didn't create enough. Our crosses were quite poor or they defended really well.”
In the second half West Ham were playing against 10 men, but Southampton held firm to claim another three points.
It was the fifth consecutive clean sheet that the Saints have collected, but the defeat was a damaging one for Bilic’s side.
West Ham are now only two points ahead of Southampton, as they look to protect their place in the top six of the Premier League table.
The Hammers’ next match comes against Liverpool in the FA Cup, before they take on Norwich City in the league on Saturday.