Ronald Koeman's Southampton sit third in the standings through 24 matches after Saturday's late 1-0 win at QPR.
Only six points separate Southampton (45) and sixth-placed Liverpool (39), with Manchester United (44), Tottenham (43) and Arsenal (42) all in the hunt for UEFA Champions League football next season.
There is a feeling that Fonte's team-mates will struggle to maintain their top-four charge with their big-spending rivals circling but the 31-year-old Portuguese centre-back has put the pressure on the chasing pack, claiming Southampton have what it takes to be there at the pointy end of the season as they continue to defy the odds.
"Those teams have all the pressure in the world," said Fonte.
"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."
