The Hammers were on course to make it three home wins in a row after Glenn Whelan headed the ball past his own keeper midway through the second half.
But a mistake from Adrian saw Stoke draw level when Bojan Krkic got in front of three defenders to volley the ball into the back of the net.
Antonio says the team have got to learn from their mistakes and work harder on maintaining their lead in the future as they now prepare for a tough run of fixtures which include Tottenham, Manchester United, Arsenal and Liverpool.
Antonio said: “These are two points dropped. We made a mistake for their goal and when we get on top we need to keep it going and hold onto the lead.
“There are no easy games in the Premier League and we just need to keep working hard over the international break and prepare for the Tottenham game.”
Antonio is still disappointed that he was not able to claim his sixth goal of the season after it appeared that he rose the highest to direct a header past Stoke keeper Lee Grant.
But after reviewing the incident, the Premier League quickly awarded it as a Whelan own goal.
After starting the season with five goals from five games, Antonio is desperate to get his name back on the scoresheet and hopes for better luck in the big London derby at White Hart Lane on 19 November.
Antonio added: “I saw it again on the big screen and headed the ball into the far corner and it should be my goal.
“It is very frustrating because you go out there and try your hardest. I had been on a bit of scoring drought so I thought I had ended it on Saturday.
“I was looking forward to celebrating that goal but there is nothing I can do about it now and I will keep going in the next game.”