The Saints chief only took charge at St Mary’s in the summer when he replaced Claude Puel in the dug-out, but the Argentinian has seen his position called into question as the side are without a win in their last nine Premier League outings.
The Saints head to Watford on Saturday lying outside the relegation zone on goal difference alone and Pellegrino is looking for the squad to pull together to try and haul the club away from danger.
“The pressure is part of the job for every single manager, the biggest risk is to work in football,” he told reporters.
“We need results, results are everything, I am doing my best. We are not in a good moment but everyone in the squad is conscious that we need to do more.”
A goal apiece from James Tomkins and Luka Milivojevic handed Crystal Palace a crucial 2-0 win over Huddersfield at the John Smith's Stadium on Saturday evening.
Manchester United bounced back from their Champions League exit as they beat Brighton 2-0 at Old Trafford on Saturday night to reach the FA Cup semi-finals.
Tottenham reached the FA Cup semi-finals after they cruised to a 3-0 victory over Swansea in their quarter-final clash at the Liberty Stadium on Saturday.
Premier League basement club West Brom squandered the lead as they suffered a 2-1 defeat to Bournemouth at the Vitality Stadium on Saturday.
Chesterfield boss Jack Lester felt his side were unlucky not to claim all three points after their 1-1 draw at Cheltenham.
New Swindon manager Phil Brown revelled in his side's victory at Cambridge in his first game in charge.