The Dutch defender handed in a transfer request earlier this week, and according to the Mirror will miss Southampton's opening game of the season on Saturday when they host Swansea City due to a "virus".
The Saints had two good opportunities in the opening five minutes alone, firstly through a Ryan Bertrand corner from the right in the first minute that found Manolo Gabbiadini but he glanced his header off the angle of the post and bar.
But it's a fair bet that the Gabon global will soon be a permanent fixture in the Saints team if this is the best that his new team-mates can do. "The only thing that's important at the moment is the Gylfi Sigurdsson situation".
For Pellegrino, the challenge remains just how to find goals in the team.
Swansea were mired in a Premier League relegation fight for much of last season, with Clement's arrival in January the turning point in their campaign.
The Argentinian was appointed after Southampton sacked Claude Puel, who guided the Saints to the League Cup final and eighth place in the Premier League last term, with club officials wanting a more attacking style of football than that played under the Frenchman.
"We never concede any counter attack and I think we did a good performance but in football it is effectiveness and you have to put the ball inside (the net) and we couldn't and we have to keep going".
"They also want to press higher up the pitch and it will be really tough for us".
"As a manager you can work in the way how to create chances, how to play in what areas in the corridor in front of the defenders and behind them", he reflected.
Swansea boss Paul Clement said: "It was a hard afternoon, they had a massive amount of chances, set-play after set-play and we suffered at times".
Towards the end of last season they were frustrated with the lack of goals, but Pellegrino enjoyed a warm welcome and a lot of patience for his team whose efforts were rewarded with warm applause as they left the pitch. Every game we play we have to try to get points on the board and look to play better.
"I think we did a nice game".