The Citizens would have secured a well-earned victory had Gabriel Jesus last-minute goal not been ruled out by VAR, but Spurs left the Etihad satisfied with a draw after Erik Lamela and Lucas Moura cancelled out Citys goals.
Speaking to Standard Sport, Winks said of the reigning champions: "Theyre an excellent side, theyre champions and you have to respect them but like all sides they have weaknesses and I think we exploited them, especially from the corner.
"We know how good we are. We know were a top side but when we come to places like this its important to get a result.
"At times it was messy, it was difficult but thats what you have to do, especially at City. You expect City to have a lot of possession, which they did. But its important when you come here to weather the storm when youre under the cosh, to stay in there and I thought we did that fantastically.
"I think they [City and Liverpool] should worry about us. Weve shown in the last few years we can compete with the best teams in the Premier League and Europe. Its important we do that on a consistent basis this season and its important we go to places like City and Liverpool and get results.
"The manager doesnt allow fear in us. We dont go into any game beaten mentally. We go into every game knowing we can win and we can outperform them. Our mentality going into every game is to be on the front foot, press and try to win. Thats probably why we came away with a good point."
Tottenham have had a positive start to the season, earning a 3-1 victory over Aston Villa in their opening fixture before this weekends draw against title favourites City.
The north London side return to the Tottenham Hotspur Stadium this week to face Newcastle United who, by any measure, have had a terrible start to the season under new manager Steve Bruce.