The new season offered little to be excited about from an attacking perspective as Swansea only managed two shots - neither on target - in the entire 90 minutes at St Mary's.
From that point of view, a scoreless encounter with Swansea might not seem like the most encouraging start for Pellegrino, particularly as it meant the Saints had still not scored at home since a 3-1 league win over Crystal Palace on April 5. Every game we play we have to try to get points on the board and look to play better. We've lost twice, the game against Manchester United that we mentioned above, and our very first Premier League match at Manchester City - losing 4-0.
"We had enough chances to score a goal and if we scored it would have been a totally different game and then we would have scored a second", he continued.
The Swans have failed to score in six of their 10 Premier League contests against Southampton.
"When we're in front of goal we just need to be clinical and more aggressive to score a goal".
Is the fixture a low or high scoring one?
"I think all of us at the club, the technical director, me as a manager, we know that Virgil is an important part of the club".
"We did everything to win the game but we couldn't".
Southampton have never won an opening day home fixture in the Premier League.
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".
Southampton have won six of their last eight meetings with Swansea in the Premier League (W6 D0 L2). They're unbeaten in their last five.
Paul Clement believes that a move to take Gylfi Sigurdsson away from Swansea City is getting closer as he waits to bring in further new signings.
I'm debating between a 1-1 draw and a 2-1 defeat.
Southampton will be looking to record their 1000th home league win in this match, since joining the Football League Third Division South in 1920-21 (P1881 W999 D485 L397).
"It's something that we have to continue working on, and keep going, but in parallel I am really happy with the performance", said Pellegrino.