Ipswich boss Paul Lambert, who won two promotions in his three years in charge at Carrow Road, was given his marching orders before half-time after a touchline fracas that also saw Norwich head of performance Chris Domogalla sent to the stands.
Farke said: "I have a lot of time for Paul Lambert and 95% of the Ipswich staff are fine but there are one or two guys - you can lose a game, but show a little bit of class, quality and style.
"I was a bit annoyed to be honest with how they handled it. Respect human beings and the words you choose, because there are children around and there are more important things in life than football.
"Some of their staff who were not so much in the spotlight - my feeling was they wanted to use today in order to prove something and I think you'd better not do this when you're in this position in the league."
Lambert, who said he did not have a problem with referee Peter Bankes' decision to show him a red card, responded: "I don't think he should be commenting on my staff. I certainly won't have him talking about my staff. He should look at his own staff first before he comments on anyone else's.
"The referee sent off the wrong guy for them. It wasn't that guy that I was arguing with."