The Broncos were behind 28-12 against Cronulla in the 54th minute on Sunday at Suncorp Stadium but fought back to win 34-28.
Their victory was full of character and resilience after a month ago they had slipped to 11th following six losses in seven games.
The Broncos were written off at that point but a 44-14 win over Gold Coast, a bye and the win over the Sharks have put their finals hopes back on track.
"I put it down to a lot of outside noise that said we couldn't do it, wouldn't make the top eight and weren't a finals team," Staggs said.
"We just flipped it all back onto them. We are fighting for one another. It was a good comeback. The more they hate on us, it feeds us."
Staggs, 26, inked a new three-year deal last week and said he was glad to have his future settled.
"I didn't want to leave. When I knew I was coming off contract I did have a look around, but I went back to my family and partner and said this is where I belong," Staggs said.
"I have been here for eight years and this is home for me. I have loved every minute of it and the bunch of boys I have made friends with are for life. I just couldn't leave.
"The club itself and the fans are a big part of it as well. I am happy it is all done and I am happy for three more years."
Brisbane host the fourth-placed Warriors on Saturday and must win if they are to make a realistic push for the vital top four themselves.
The Warriors, on 24 points, are six points ahead of the Broncos but still within reach. Brisbane are seeking three wins in a row for just the second time this season.
If they replicate the final 26 minutes against the Sharks when they play the Warriors, the Broncos will be in a good position.
"The second half, we went out and just knew we had to stick to the game plan," Staggs said.
"They scored that early try in the second half and we looked at each other on the tryline and we just said, 'The only way we can get out of this is on our own'.
"We all went back to doing what we do best. We jumped on each other's back and found a way out and it was a good win."