The 26-year-old was wanted by champions Leicester City last month and attempted to push through a deal by handing in a transfer request at the Riverside Stadium.
However, Boro refused to let the Uruguay international leave the club and, having talked over the situation, Karanka is adamant that he still has full confidence in the forward.
"Yes, we had a meeting, but the best way to show a player how important he is for the team is not on a sofa in a meeting. It is that he is playing and I am giving him all my confidence, as I have tried to do since he arrived here," he told reporters.
"It's not difficult for him because I have always said in press conferences here and in my meetings with him how important he is for the team, and he knows. It's not a reason or an excuse that you can tell him. He knows because I have shown him how important he is for this club, for this team, as he was when he came here.
"The team, the club have helped him to reach that level and now with him, we know we have three or four really important months in front of us and he knows he is really important in this team. He gives us a lot of things with the ball, set pieces, a quality and pace, so with him on the pitch, we are a better team."
Boro, who face Oxford United in the FA Cup fifth round on Saturday, are yet to win a Premier League game in 2017.