The Saints go into the game off the back of two defeats and the former Alaves boss is keen for his side to get back on track, starting against Rafa Beintez's side.
Speaking ahead of the match, Pellegrino said that he is hoping to see his goal-shy side finallly click.
'The game on Sunday is really important for us,' Pellegrino said. 'It is true that every single game is important, but of our next four games, we have three at home and we have to push ourselves to get the points we deserve in other games.
'I would like to win as many games as we can, but the position right now does not mean anything. We have to keep going because we are dominating and controlling the games.
'If we drew our last match against Stoke we would not be talking about changing a lot of things. Sometimes you think you have to change things after you have not got the result. But we have to analyse what we are doing right, what we are doing wrong, and we have to keep going with this mentality.
'We have to improve not just in attack, but also in defence and in a lot of areas we can be better. Hopefully it will be a good possibility this Sunday to show that we are better than the last game.'
Pellegrino will go up against former manager and close friend Rafa Benitez. The Newcastle boss managed Pellegrino at Valencia and Liverpool, before adding his to his coaching ranks with the 'Reds' and later with Inter Milan.
The 46-year-old says he is keen to catch up with Benitez, though he admitted that the pair probably won't share a beer post-match.
'Rafa doesn't drink too much, so I will invite him to have a Coke after the game,' Pellegrino joked.
'I try to learn from everybody. When you consider I am really young in this profession, I am only starting, and I want to learn every single day to try to be better.
'Rafa doesn't need too much advice from me because he is a manager with a lot of experience in the Premier League. He has worked for 20 years, more or less, at different situations. It will be really nice to be with him again and to play against him.'