The Hammers headed into the campaign full of optimism following an impressive first season under manager Slaven Bilic last year.
Things have not gone well for them, though, as they have struggled to replicate that form.
They are currently 15th in the table and five points from safety, with wins in their last two games helping them to push away from the relegation battle they had been threatening to get dragged into.
There is hope the victories have helped to turn things around but Ogbonna refuses to get his hopes too high just yet.
“I don't know how much this will turn our season around,” he told the club’s official website.
“I want to stay focused on the present because sometimes our mistake was sometimes setting our expectations too high and we have to stay focused on the next game."
It remains to be seen if the two wins do signify a change in West Ham’s fortunes this season.
They have an excellent opportunity to make it three victories from three in their next game when they take on Swansea City, who currently sit 19th in the table.
A win in Wales could see the Hammers move as high as 10th; a far healthier position than they have occupied in recent months.