The home side had the better of the chances in wet and windy conditions, but could not find a way past Hammers goalkeeper Jussi Jaaskelainen.
The Finn made a series of excellent saves, most notably from Dani Osvaldo and Morgan Schneiderlin, as Saints failed to find the net for the second successive match.
"It was a very frustrating afternoon because we did everything we could to try and win the match," Pochettino told Saints Player
after the game.
"We have to accept that this is something that happens in football because we couldn’t have done any more. We created chances but they wouldn't come off.
"This was our fourth game of the season and we will continue to improve.
"I think we were much brighter and quicker where the tempo was much improved in the second half, and that is how we want to play," he continued.
"How we move the ball, the speed and tempo was much better, so we are pleased with that and we just need to keep that up.
"I am pleased that we showed we are solid at the back, so hopefully the dynamic will change soon and we will start getting goals and victories."
Pochettino brought Jay Rodriguez into the side for the game as he looked to improve on a their narrow defeat to Norwich a fortnight ago.
Rickie Lambert and Dani Osvaldo retained their places up front and, despite drawing a blank for a second successive game, the manager was impressed with how his front three are beginning to combine.
"There has been a lot more chemistry between all of our attacking players," reflected Pochettino.
"Osvaldo arrived late to the group, so it is natural that it takes a little longer to get into the form of the team.
"You can see they are starting to mix well together, so it is only a matter of time before things start to work out positively for us."