The Saints, who are currently three points above the relegation zone in the Premier League table, have picked up five points from a possible 18 since the Argentine took charge in January.
"Speaking in a very objective way, I think the team deserves a lot more than to have just one win from these six games," Pochettino told reporters.
"I haven't set myself a number of points to achieve to stay up. What is my absolute desire is to win the next game."
Southampton continue their fight against the drop on Saturday when they travel to Norwich City.