Llorente scored on his return to the Liberty Stadium after leaving the Swans for Spurs last summer.
"I think it was difficult for the team and for him to play in these conditions," Pochettino told Sky Sports.
"I am happy for him to help the team to achieve three points. When a new player arrives in a team where the dynamic is so clear always it is a struggle to find the possibility to play.
"He's very professional and I'm so happy that he helped us achieve what the team wanted."