The reverse meant that the Saints have won only one of their last nine Premier League games.
But their finishing let them down.
Talk of Saints pushing for a surprise European spot has diminished following their recent poor form, but Pochettino is not a worried man.
"Rome wasn't built in a day," the Southampton manager said.
"We have been facing some of the top sides and that has been tough.
"We are a young side and we are still learning. We have to keep on believing on our style of play."