The Italian international had been linked with a move to Goodison Park throughout the summer, with United knocking back a number of offers for the player.
There had been speculation that the Merseysiders would make a definitive beat-the-deadline move before the 11pm cut-off point on Friday.
Speaking after his side's 2-2 draw at Sheffield United, Dyche - when asked if the club had made a move for Gnonto or other wing targets at the end of the window - commented: "We weren't close enough to any situation. The truth is that, certain parameter guidelines, we are now at.
"The club is not in the spot it was two or three years ago, I think that has become apparent.
"(But) I have always thought you 'manage what you can manage' and manage the realities. They are the realities.
"On the other side, don't forget, if you know the transfer window that it makes news and all that... But when everyone is fit and you look at our group, you go 'right there's still some very, very good players' here and a number of them.
"So sometimes that still gets overlooked. I believe in what is here and the players that are here. So far this season, I believed we have delivered way better than we have got back."