Lewis collected a second yellow card in the 37th minute of the match, with referee Slavko Vincic deciding the 17 seconds he took over a throw-in was far too long.
The Slovenian official seemed to have forgotten he had already booked Lewis for a tug on Breel Embolo, but after a pause he produced the red card to change the nature of the game - ultimately settled as Steven Zuber and Christian Fassnacht scored in stoppage time of either half.
"I don't think I'll say what I want to say without getting into trouble to be honest," Baraclough said. "I'm annoyed and appalled by the decision to give someone a yellow card without even warning the player.
"Whether he thinks it is time-wasting or not, you normally go up to a player and tell him to hurry up or you'll do something about it. But he didn't get any warning at all.
"Whether he has been swayed by Swiss players or the crowd, I think the occasion got to him. I think he realised when he pulled out the yellow card that he had forgotten he had already booked Jamal. I think their players would say the same sort of thing. It's changed the entire complexion of the game."
Asked if he had been able to speak to the officials during or after the match, Baraclough added: "No, none of the officials wanted to give any explanation. And that's not lost in translation, they can speak English.
"It's something we have to take on the chin, but you expect officials at this level to get decisions right more often than not. I think we were on the end of a poor one."
Defeat leaves Northern Ireland six points behind the Swiss in the fight for second place in Group C. With only three games remaining, their chances of earning a play-off place are all but over.
And for controversy to come in a World Cup qualifier against Switzerland - just as it did four years ago when Ricardo Rodriguez's penalty for a disputed handball settled the play-off between these two nations - was a painful irony.
"Is that something that happens with a so-called minnow against a bigger side? Coincidence or not, it's hard to take at this moment in time," Baraclough added.
"The Swiss are a good football side, they've got good players and really good individuals. We knew it was going to be a tough game tonight so you need decisions to go your way. I think we've been on the end of a very, very poor decision."
Northern Ireland were not the only ones surprised by Lewis' red card. Both benches had jumped up when Vincic blew his whistle, and Switzerland coach Murat Yakin admitted he feared one of his own staff members was in trouble.
"I actually didn't realise the situation," said Yakin, whose side had an early Denis Zakaria strike ruled out for offside. "I was surprised. My staff members were jumping up and getting excited and I thought when the red card was shown it was to one of my staff members and not for the player.
"But overall I don't think this was decisive for the match. With our performance we controlled the match already before. We were very focused, even after the offside 'goal' in the first minutes, we didn't stop.
"We had more pressure, we tried to attack, and maybe the only thing we can say is we didn't benefit from all of our chances to score. We fought to the end and created more opportunities."
Former Northern Ireland international Neil Lennon tells Sky Sports:
"The referee doesn't warn him, doesn't blow the whistle, but he walks over to him, blows the whistle, and gives him a second yellow card.
"It's shambolic, I've never seen a player given a second yellow card for time-wasting on 36 minutes in any game in my life."
Former Northern Ireland international Chris Brunt:
"The referee, with the crowd booing, has pulled the yellow card out and then realised he has to send him off. You can half see it on his face."
Northern Ireland travel to Bulgaria on Tuesday night in a must-win World Cup qualifying encounter, live on Sky Sports Football; kick-off at 7.45pm.