Wallace, known as "Bubba," hugged his mom and sister in the Daytona International Speedway media center afterward and started crying before speaking Sunday night. His family didn't get to see him right after the race because he went to the infield care center after the crash with Hamlin.
"I'm so proud of you, baby," his mom said between sobs.
"You act like we just won the race," Wallace told her.
"We did win," his mom said.
The driver didn't feel like a winner, but he felt like he did something he never knew he would get an opportunity to do: competing in the NASCAR Cup Series.
"I just try so hard to be successful at everything I do, and my family pushes me each and every day, and they might not even know it," Wallace said. "But I just want to make them proud. Second is horrible, but it's still a good day."
Wallace, the first full-time African-American driver since Wendell Scott's last complete season in 1971, received a call from Hank Aaron before the race and received a tweet -- and a follow -- from four-time Formula 1 champion Lewis Hamilton, who also is black.
"[I was] fan-girling out," Wallace said. "I look up to him. ... He's just a genuine badass in what he does, so that was cool [that he followed me], and then he sent out a tweet, and I got weak at the knees."
Wallace didn't have the same gratifying feeling about his friend, Hamlin, after the race. Hamlin and Wallace were side-by-side battling for second, and Hamlin ran into Wallace after the race.
"He might need to take some Adderall for that one," Wallace said on TV afterward, referring to Hamlin's comments last week on a Barstool Sports podcast that 70 percent of drivers take medication to help focus -- a statement Hamlin later said was a joke.
Hamlin said on his in-car radio to his team, as well as to the media afterward, that their contact before the checkered cut his tire, and he couldn't steer his car.
Wallace was never in much of a position to win the race, giving Austin Dillon the push Dillon needed to win in the green-white-checkered finish. But if Dillon had wrecked when he had contact with leader Aric Almirola on the final lap, Wallace and Hamlin would have had a drag race to the win.
"I got the rookie stripes for a reason, so making some of those moves today, I was a little bit delayed and a little bit late and luckily kept it out of harm's way," Wallace said. "It just all comes with time. ... I have the attitude and just the confidence to win every race that [I] enter.
"We all know that's not going to happen, so jumping in tonight we had the same attitude, but I knew the circumstances and how this plays out and moves that you have to make and the defending and blocking that you do. I've never done it at this level."
The only NASCAR finish by a black driver better than Wallace's second-place finish was Scott's victory in the Jacksonville 200 in 1963. Scott also finished 13th in the 1966 Daytona 500 race, the previous best finish for a black driver at Daytona.
Wallace drove in four races last year for Richard Petty Motorsports as a substitute for Almirola. He ran well enough to earn the full-time ride in the No. 43 car this year after Almirola left for Stewart-Haas Racing.
"That's a heckuva start," Petty said. "We have a new car, a new driver. The 3 [of Dillon] and 43, [it's] been a long time since they've been on top of the board. ... He was in the race all day long. That was good."
It has been a long couple of months for Wallace, who has had cameras following him for various broadcast features and a Facebook video series. It has been draining for him being followed so often and the focus on him with the historic nature of his landing a Cup ride.
He said a call from Dale Earnhardt Jr. motivated him.
"He just had the words to bring that positive light back up that I try to carry with me every day," Wallace said. "He says I'll have the opportunity to do things outside of this sport that not really anybody else can, so take that, run with it and set yourself up for 10 years from now [to] look back on it and see how you did."
Then he got advice from Aaron with a phone call right before he got in his car.
"He just said, 'Hey, good luck, and just have a good race today,'" Wallace said. "He knew that we were pressed for time, and it was five seconds, and that's all he said.
"That was really cool. ... That's awesome."
The Associated Press contributed to this report.