The 22-year-old midfielder, who has been linked with Newcastle and Wolves, was out of contract in the summer and free to talk to other clubs this month.
But instead Lallana signed a new four-and-a-half year deal at St Mary's on Friday, and 24 hours later helped the League One promotion chasers dump top-flight Blackpool out of the FA Cup.
"It's always good to test yourself against Premier League opposition, even though they made a few changes," said Lallana.
"So did we because there are a lot of games coming up, and I felt we thoroughly deserved the win. We had a lot of chances and we got there in the end because we kept persevering.
"I feel I can push myself to the limit every week when I am playing and it's brilliant to play against Premier League teams to see if you can play at that level. Obviously as a team we want to push on forward to get to that place."
Source: PA
Source: PA