Having led the match early on, Spurs needed a late equaliser to salvage a 2-2 draw against the Merseysiders at White Hart Lane, with the Toffees also outside contenders for a place in the Champions League spots.
However, with Chelsea and Arsenal also winning over the weekend, the German admits that Spurs really needed to win.
Asked if Tottenham had needed to beat Everton, Holtby told The Telegraph: "I think so, yes. But the positive is that we didn't lose to a rival. It was a good performance in the second half but, if we want to play in the Champions League, we want to win those games.
"We've still got decisive games against City at home and against Chelsea away. Even the games against Southampton and Sunderland, these games we have to win. After 38 games, we have to stay in the top four.
"I have big faith in us because we have a quality side. Of course if you look at the watch and it's still 2-1, you want to get that goal, you're a little bit nervous then but I think we kept our calm. That's why we got the goal. Our patience was big. The past is not in our favour but I think this team has so many qualities to get in the Champions League. If you view the season, all the effort we have put in, I think we deserve it."
Spurs turn their attention to the Europa League on Thursday when they travel to Basel.