Leicester, who beat Manchester City on Saturday to go five points clear at the top of the table, also battled against relegation last season but put on a late charge for safety.
Sunderland are second from bottom and fought back against Liverpool to win a point away at Anfield on Saturday, with Defoe scoring late to draw the teams level at 2-2.
"(Leicester's) story is unbelievable. But you do think, if they can do that why can't we?" Defoe told British media.
"We have such a strong squad here now, the new boys have come in and been brilliant."
"The team spirit is great and if we carry on working hard we will get results and hopefully get them soon."
Defoe's goal against Liverpool was his sixth in his past six league games, and the 33-year-old said he was enjoying his role as striker under manager Sam Allardyce after being deployed out wide under the Englishman's predecessor, Dick Advocaat.
"The previous manager played me wide on the left, and I'd never played there before in my life, even at school. It was a bit strange, playing at full back when you've always been a forward," Defoe said.
"This one (Allardyce) came in and even though I have never played under him, he knows me. He's changed a lot of the team, as well as the intensity levels and fitness."