The Saints drew 1-1 with Manchester United at Old Trafford on Saturday, to maintain their place inside the top four in the division, before Manchester City's win over West Ham United later that day.
When asked if his side can stay there for the remainder of the season, Pochettino told reporters: "Why not? We want to keep on believing we can do well. We're on a positive run and the sky is the limit.
"Getting a good win [against Liverpool] at Anfield and a positive draw today is amazing for the club and shows how we want to move forward - and it gives the young players belief."