Ronald Koeman’s side beat QPR 1-0 on Saturday and are now third in the Premier League table after Manchester United, Arsenal and Liverpool all dropped points over the weekend.
It was a series of results that left the Saints in third place and Fonte said: “Those teams have all the pressure in the world.
“For us, no one really believes in us, no one really thinks that we’re going to get there. But we as players and the group believe in ourselves and we’re going to be fighting for that.
“It’s going to be like this until the end I think. As we said before the game, we just need to keep going game by game, keep digging, grinding the results out and we’ll see in the end where that takes us.”
Southampton dominated the first half at Loftus Road but left it late to seal all three points as Sadio Mane struck in the third minute of stoppage time.
“It was a massive goal, it keeps us in the fight,” Fonte added.
“The mindset was, no matter what, we needed to get three points, so we were ready for the battle and I think we showed that. We competed and we won many second balls.
“With our talent up front and the quality our players have showed, we were a threat with Sadio one side and (Eljero) Elia the other side. We have players that can hurt teams.
“It’s a shame that we couldn’t get the goal earlier, but we kept going and at the end we got the result.”
The only negative for Southampton was defender Matt Targett taken to hospital after the left-back suffered a head collision in the first half.
Koeman said after the game that Targett’s condition was “under control” and the 19-year-old tweeted on Sunday morning: “Thanks for all the nice messages!!
“Massive headache today!! Great 1-0 win for us yesterday #saintsfc #WeMarchOn”