Rafael Benitez hailed the "fantastic" impact of Liverpool captain Steven Gerrard on the Anfield club's opening Champions League group match in France.
Gerrard's first was a stunning 25-yard effort before he put away a twice-taken penalty.
Manager Benitez said: "Gerrard's first goal was fantastic. But the whole team worked really hard for the victory.
"It was important to get our group matches off to the right start, but clearly we can play better.
"However, we are now in a very good position and if we can win our home matches in this group we should qualify for the next stage of the competition.
"But we had to work very hard for the victory. Marseille are a better side than when we won here 4-0 in last season's competition, and they proved that with the way they played and the amount of chances they created.
"We were able to keep Gerrard and Fernando Torres on the pitch for about an hour after their recent injuries, and then it was left to the rest of the team to defend the lead.
"We did that well, everyone played their part and although we know we can play much better, it is still an excellent start to the group."
Marseille coach Erik Gerets also hailed Gerrard's influence on the game.
He said: "He is a world-class player and he proved that. Only players of that quality can score goals like that.
"We had just scored and we should have been focused on protecting that advantage. But players of Gerrard's quality are capable of scoring goals like that and he changed the course of the match.
"I am very disappointed with the result. We created enough chances to have won. I am angry with the outcome because we were unable to make use of our good play and the opportunities we created.
"It is really annoying, we cannot afford to lose home games like that if we are to qualify. Now we must play Atletico Madrid next away from home.
"They have already won their first match and if we cannot win in Madrid, we will be facing a very difficult task to qualify for the next stage."