A 2-0 win at Everton meant the Black Cats recorded back-to-back victories for the first time this season and the result lifted Dick Advocaat's side two points clear of the relegation zone.
"It was a must-win game to be honest, we knew we had to win," said Defoe, who made sure of three points with an 85th-minute effort after Danny Graham's fortuitous first goal for the club 28 months after joining.
"We still have an important game next week (at home to Leicester) but it is back-to-back wins and we are delighted to have done it.
"I think it has added a bit more pressure on the sides around us now.
"There was a lot of pressure on us to get a result and we handled that and that is credit to everyone at the club.
"We were solid, organised and patient as this is a difficult place to come. It was never going to be easy, so to win here 2-0 was credit to the players.
"It was impressive to get the result - it doesn't matter how you do it. There was a lot of pressure in a must-win game and we can go home happy.
"You need a bit of luck, and yeah and I think you get that luck when you work so hard as a team."