The Potters took the lead after just 13 minutes thanks to a goal from Jonathan Walters and should have gone on to get more as they were the better team in the first half.
They were made to pay as the home side hit back with Joey O'Brien levelling matters just after the break on 48 minutes and Pulis admits a second goal when they were on top would have made the difference.
"I thought we played really well in the first half but fair play to West Ham," said Pulis. "Their crowd really, really got behind them and we showed a lot of resilience in the second half.
"The worst thing that happened to us was half-time. We watched West Ham defensively and noticed one or two things we thought we could exploit. We've practised it about five times over the last few days.
"We can't turn those draws into wins. If we had got the second goal it would've taken the pressure off the lads."