Braces from Harry Kane and Christian Eriksen and a goal from Son Heung-min secured Tottenham only their second victory in 11 games.
Spurs were knocked out of the Champions League after a 2-1 defeat to Monaco on November 22 and lost to London rivals Chelsea last weekend but the result sees them move just one point behind Arsenal in the league table.
"I think that we fully deserved the result," Pochettino said.
"We dominated, we created chances, they didn't shoot, they didn't create chances and I think it was a very good performance
I am happy because we got three points which was important after Chelsea and Monaco.
"I don't believe it was the best (performance) but I think it was good because it is always good to get three points and keep near the top.
"We have ahead very important games and confidence is back.
Tottenham were awarded a penalty on 38 minutes when Kyle Naughton appeared to bring down Dele Alli but replays showed there was a suggestion of a dive from the Spurs midfielder.
Pochettino insisted he had "not seen the incident" but Swansea manager Bob Bradley thinks it was a bad call by referee Jonathan Moss.
He said: "I think it was the wrong decision, I don't think the referee was in a very good position and certainly it was a game changer.
"I haven't seen a good enough replay (to say whether he dived).
"We told (Naughton) right away that it was a wrong decision and to put it behind him."
The result sees Swansea drop to the bottom of the Premier League standings, with just one win in their last 13 games in all competitions and Bradley knows they fell short.
He said: "I am pretty honest and today we were not good enough.
"We knew that it was going to points here, it is difficult for everybody to get points at White Hart Lane.
"We also knew that Tottenham was a team that was going to really press with intensity
They put us under the most pressure.
"We just weren't good enough, we were second best most of the time and when they pressed us we couldn't get the first pass out of pressure.
"There is a lot there in which we need to work on to get ourselves out of pressure now we have to focus on the important run of games."
Source : PA
Source: PA