The Saints now haven't scored in almost 550 minutes of football at home, something which makes for bleak viewing with their upcoming game against West Ham United set to also be played at St. Mary's.
Pellegrini resisted the temptation to start with Mario Lemina, the striker signed from Juventus in a club record £18.1million deal earlier in the week.
SOUTHAMPTON, ENGLAND - AUGUST 12: Dusan Tadic of Southampton and Leon Britton of Swansea City battle for possession during the Premier League match between Southampton and Swansea City at St Mary's Stadium on August 12, 2017 in Southampton, England.
Southampton have won six of their last eight meetings with Swansea in the Premier League.
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 controlled the ball, created chances but this is football - you have to get goals and we couldn't do so.
"As a manager you work out how to create spaces and chances behind defences, in front of them, on the overlap and in wide areas, but to have the accuracy to score a goal is something that is hard to work on".
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".
"It's something that we have to continue working on, and keep going, but in parallel I am really happy with the performance". The last-gasp defending was good but we didn't use the ball well enough further up the pitch.
"We've got a lot of thing that we can improve".
"Swansea is a good team, they were ready to attack us but we were well balanced and that was the key to controlling the game in the second half". Every game we play we have to try to get points on the board and look to play better.
"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".