The West Ham United midfielder was controversially sent off for a challenge on Dwight Gayle during the Premier League game against London rivals Crystal Palace at the Boleyn Ground earlier this month.
The red card to the 26-year-old Senegal international, who can also play as a defender, was later rescinded by the FA, and the former Anderlecht star was able to take part in the league match against Arsenal at the Boleyn Ground at the weekend.
Andy Carroll scored a stunning hat-trick against the Gunners on Saturday afternoon to help his side secure a 3-3 draw in the London derby.
Former Sky Sports presenter Keys, though, believes that the England international striker should have been sent off in the match and should not have been on the pitch to score three goals.
Keys has also explained why the FA were wrong to rescind the red card given to Kouyate against Palace.
“Carroll was fantastic, but he shouldn't have been on the pitch after his lunge at Koscielny early on,” Keys wrote on his website. “That met all the criteria for red. It was dangerous. He had absolutely no chance of winning the ball.
"He caught Koscielny late, first with his right foot and then in a scissor movement with his left. It certainly did 'endanger the well being of an opponent'. Carroll was lucky. He should've gone. So why didn't he?
“It was early on, so Craig Pawson probably gave him the benefit of the doubt. Or - was he scared to make a decision because of what happened to Mark Clattenburg recently? Clattenburg was made to look a fool when three X-pro's overturned his decision to send Kouyate off the previous week.
"That was poor. It completely undermined him. We can argue all day long about whether Clattenburg's decision was correct or not - but it should never have been overturned.”
West Ham are sixth in the Premier League table at the moment with 52 points from 32 matches, five points behind Manchester City, who are currently fourth in the standings and occupy the final Champions League spot.