Brees, 25, earned his first Pro Bowl selection as he helped transform last year's 2-14 Chargers into AFC West Division champs and legitimate Super Bowl contenders at 12-4.
Brees makes his playoff debut this Saturday as San Diego hosts the New York Jets.
"You cannot give up," he said. "You always have to have that attitude that your goals will be achieved.
Drew Brees is the AP comeback player of the year. (AP Photo/Lenny Ignelzi)
"You've just got to keep grinding away. And if not this year, then next year.
"And if not next year, then the year after. You just keep believing and it will happen."
Brees, a four-year NFL veteran, finished third behind Peyton Manning and Daunte Culpepper with a 104.8 passer rating – a remarkable 37.3-point improvement over the previous season.
Brees completed 65.5 per cent of his pass attempts (262-400) for 3,159 yards and 27 touchdowns with only seven interceptions.
"I set out with a goal and a purpose in mind," he said. "That was, first of all, to lead this team to a championship.
"Along with that, to try to become one of the best quarterbacks in this league, although neither of those goals have been accomplished. But that's the path, that's what I strive for."
Brees received 181/2 votes from The Associated Press panel of writers and broadcasters compared to just 10 for runner-up Mark Fields, a linebacker with the Carolina Panthers.
"I just think it will be very satisfying to him, considering the situation that he was in at the end of last season," figured Chargers backup quarterback Doug Flutie, named 1998 AP comeback player of the year with the Buffalo Bills.
"Redemption, a feeling of accomplishment (and) all that. Just that it's showing a lot of resolve and bouncing back up off the floor and taking the shots and jumping back in and going after it."
Amazingly, Brees wasn't named San Diego's starter until six days prior to the season opener.
Chargers general manager A.J. Smith publicly proclaimed that the Chargers needed to "upgrade" at quarterback and even drafted highly-touted Eli Manning first overall last April, only to trade him to the New York Giants for the rights to Philip Rivers.
Had Rivers not held out for half the preseason, Brees might not have started.
"I viewed that as if I'm going to upgrade it myself and that's going to be the upgrade at quarterback," he said.
Brees is a 61.2 per cent passer with 802 completions in 1,309 attempts for 8,772 yards, 56 TDs and 38 INTs in 44 appearances, including 42 starts, since being drafted in the second round – 32nd overall – out of Purdue in 2001.
with files from Sports Network