The Nerazzurri are fifth in Serie A, three points adrift of a Champions League place and 12 points behind league leaders Juventus.
"Yes, I still have confidence [in Stramaccioni]. We need to work hard, stay very alert and defend against attacks – especially those closer to us – in such a way so that things start working again,” Moratti told Inter.ie.
"No, I never sent any SMS," he added. "I also read this but I didn’t send anything. Stramaccioni and I had a chat."
Moratti, who became president in 1995, also commented on his club's new signings acquired during the January transfer window.
"The two from eastern Europe did very well, but I can’t say the same for [Ezequiel] Schelotto. It wasn’t his fault however as he hadn’t played for a month. He tried, but it’s not the player’s fault if he didn’t turn in the greatest performance."