Pellegrino, a former Argentina international, has faced a difficult start to his tenure at St Mary's Stadium with his side struggling for both goals and points.
The Saints will head to Anfield - a former home for Pellegrino who played and coached at Liverpool - 13th in the Premier League table, just four points above the relegation zone, and with one victory from their last six matches.
Southampton have found the back of the next nine times in 11 matches this year, and three of those have been converted from the penalty spot. Indeed only Huddersfield, Bournemouth, Swansea and Crystal Palace have scored fewer goals than the Saints this season.
But Pellegrino, who played 13 games for Liverpool under Rafael Benitez at Liverpool in 2005 before joining the Spaniard's coaching team, insists the Saints will head to Anfield in search of three points.
Asked if he intends to go on the attack against Jurgen Klopp's side, Pellegrino replied: "Yes, for sure. Liverpool and Southampton are two sides who are both comfortable with the ball, but we will try to be there and to manage the ball because this will be the key to the game.
"They will try to press high to make us feel uncomfortable and we will try to be aggressive. When you are high up it is an opportunity for us to try to create pressure and problems.
"It will be really tough because they are a good team, but maybe against those teams which are more offensive we can find more space."
Claude Puel, who was axed as Southampton manager last summer, courted criticism from the St Mary's faithful for his perceived negative approach to matches.
And despite Pellegrino's arrival from Spanish side Alaves for the new campaign, it is a hangover which has seemingly carried over into his regime.
"To build a team is something that is really difficult to finish," Pellegrino added. "It is a long transition and a process because the connection between the players does not have any limit. Even when you are winning, you will always have something to improve on.
"The best thing about the Premier League is that it is really tight and every single week you are surprised about two or three results, and that is something which doesn't happen in other countries.
"In the last match against Burnley we played well but we lost. We have to take the best moment from that game as a reference to keep going to try and do the same when we travel away to difficult places like Anfield on Saturday."
Pellegrino will be without midfielder Mario Lemina, who is nursing an ankle injury, but Virgil van Dijk will line up against the Reds for the first time since they failed in their summer approach to lure the wantaway defender to Anfield.