In-form Antonio arrived on the south coast as the Premier League's leading scorer and having been crowned the top-flight's August player of the month on Friday.
But his first club appearance in September ended in ignominy after he picked up a second yellow card in the fifth minute of added time as the unbeaten Hammers missed the chance to go top of the table.
"Look, it can happen football," said Moyes.
"Having been booked the first time, he was stupid to lunge in but these things in football happen, so we're not going to make too big a deal of it.
"He's got himself sent off and at the time it looked like the referee probably got it right.
"We always knew these sort of things could happen and they have done today."
Antonio - who had scored four goals and provided three assists in West Ham's opening three games - collected his first booking for throwing Jack Stephens to the ground in frustration following a 71st-minute tangle.
The one-time Southampton loanee was shown a second yellow card by referee David Coote for a late tackle on Moussa Djenepo, prompting cheers from the home crowd.
With a Europa League campaign to contend with this term, Moyes had spoken in the build up to the game of needing to manage Antonio's minutes having failed to recruit a direct understudy during the transfer window.
The 31-year-old will now be suspended for next weekend's league clash with Manchester United and Moyes suggested that could affect his planning for Thursday's European opener away to Dinamo Zagreb.
Asked if the trip to the Croatian champions was a chance to try other options, Moyes replied: "I think maybe you might think the other way and think you should play because he's not available for the Man United game, so there are a couple of ways to look at it.
"We don't want Mic to go weeks and weeks without playing."
Tottenham's 3-0 defeat at Crystal Palace in Saturday's lunchtime kick-off had opened the door for West Ham to climb to the summit with victory at St Mary's.
Yet the Hammers were fortunate to escape the south coast with their unbeaten record intact as lively Saints substitute Armando Broja struck a post and had a late header hacked off the line by Declan Rice.
"I actually thought today that we played some really good football in the first half but the forward areas didn't produce, didn't connect, it looked like they had all been away (on international duty)," said Moyes.
The stalemate was a third successive draw for Southampton, who are still searching for a first top-flight victory of the season and have now gone eight meetings without a win against West Ham.
Saints boss Ralph Hasenhuttl felt his side deserved more than a point following the flurry of late opportunities, which included the two near misses from Chelsea loanee Broja.
"The way we defended deep was very good and in the end we had the bigger chances today and normally we should win the game," said the Austrian.
"Yes, we had less possession, but no we didn't have less chances to win the game.
"Today the defensive work of all of our team was amazing and this is the key of staying in the game and getting a chance to win it.
"I don't think we have ever been so close to beating West Ham, a team we struggle against."