The Saints have not triumphed in the Premier League since the end of November, with a nine-game winless run leaving them just outside of the relegation zone in 17th position.
Pellegrino's future has been the subject of much speculation in recent weeks, and the Argentine admitted that 'results are everything' when questioned on his team's current form.
"The biggest risk in football is to work in football. In football you need results, they are everything," Pochettino told reporters.
"We are talking about, not just how the team is playing but budget, money and today football is not about if the team is playing well or not – or about results – it is about next season, a lot of money, a lot of business.
"I am doing my best. We know are not in a good moment but I feel that everyone in the squad is conscious we need to do more to change the situation. We have a good base to try and convert our stats to better results."
Southampton will travel to an inconsistent Watford on Saturday afternoon.