Dejan Lovren's second-half goal proved to be enough to give Southampton all three points and end Liverpool's unbeaten start to the season.
Pochettino believes they deserved the victory for their strong second-half showing as they prevented Liverpool from creating too many goalscoring opportunities.
"We are very pleased and satisfied with the performance of the team," beamed a delighted Pochettino.
"We played very well in a very tough stadium so we are very pleased with how we played.
"I think especially in the second half we were much superior to them and we developed how we wanted to play in the second half.
"We fully believed from the outset and our performance was outstanding I thought.
"The secret also was not conceding any goals."