Saturday's Premier League clash finished 0-0 and the game's main talking point came when Cattermole - back in the team after serving a one-match suspension for five yellow cards - clattered Cambiasso with a late challenge in the second half.
Sunderland coach Poyet insisted Cattermole had no case to answer, though.
"Ten years ago his tackle would have been highlighted as one of the best in England. We are going soft," he told BBC Sport.
"These people that never play football and don't have a clue are trying to make it a non-contact sport. This is football. It was a proper English tackle."
Poyet also paid tribute to the character of his team and believes Sunderland are close to fully recovering from the 8-0 hammering they received from Southampton last month.
"We used to say we were a good football team to play until the bad game we had a few weeks ago," he added at his post-match news conference.
"Now we're back to being a difficult team, we don't give the opposition too many chances which is important in football and then [you can] try to play your game.
"I think it was a typical game between two teams that are in the situation we are, not too many chances. Normally you expect one action, we had one great action in the first half with [Steven] Fletcher but it was a great save. Normally there is one quality moment or mistake.
"It was back to basics [after the Southampton loss], that day was a terrible day, it was unique, but it creates doubt in the players' minds.
"The following game [a 2-0 loss to Arsenal] we made two terrible mistakes, but we have now played Crystal Palace and Leicester away and conceded just one goal. I think we are back to normal."
