Olivier Giroud's late header denied the 'Saints' all three points, but despite the disappointment Pellegrino was pleased with the level of performance and intelligence shown by his side.
"At the beginning the feeling is that we have conceded at the end again, as it was more or less the same against [Manchester] City," Pellegrino said following the game. "But it is different because we played a good game, showed intelligence and we got a point.
"I think we competed really well, even with the changes we made and players like Jack Stephens and James Ward-Prowse who were out of their natural position. I am happy with that."
The Spaniard was also full of praise for Arsenal, insisting that they have the quality of a top four side, despite having missed out on the Champions League spots last season.
"Against this team [Arsenal] you have to play close to excellent, because they don't need too many actions to create problems but in both aspects, attacking and defending, we were intelligent and focused from beginning until the end," he explained.
"This is a really strong Arsenal side. I know this season they are are not in the Champions League, but normally they are and fighting for the top four. For me, they are still a top team.
"It's a good reference for the future and in three days we have another opportunity [against Leicester]. Hopefully we can continue in this way."