The Mahindra driver qualified third for the race on the Brooklyn Street Circuit, which became a front-row start after pole-winner Nick Cassidy was handed a 30-place grid penalty for a battery change.
After a strong defensive effort, Sims was passed by Vandoorne for second on lap 22, but looked good value for a podium place before Mitch Evans was able to find a way past four laps from the end after reeling in the leading pack.
Regardless, Sims felt that the result was a "just reward" for the Mahindra squad's efforts - and that his focus was on bringing home points rather than trying to put pressure on da Costa for a victory.
"We had good race pace - we went backwards a little bit, but I think that was more circumstantial to the way the racing was," Sims told Motorsport.com.
"My mindset was inevitably a little bit more wanting to try and score some decent points here rather than look to win the race.
"When I had Stoffel, [Nyck] de Vries and Mitch behind me, all of them probably with a mindset of 'why is this Mahindra here, I want to get past him,' they were constantly pushing me to defend a bit, and I'd have to over consume.
"And that just inevitably hurts your race pace from thereafter, you know, little by little. But I can't complain, it feels like a podium today [Sunday]. Honestly, it's a nice result and just reward for the whole team."
Sims said that his focus was on trying to balance making progress, while also trying to ensure that he was defending properly from the cars behind.
The British driver explained that he tried to be "fair but firm" with his driving - but was impressed by Evans' move around the outside which eventually cost him a podium position.
"You're trying to balance it the whole time; you've got to to look in your mirrors and be smart with what they're doing," Sims explained.
"If you just drive your own race the whole time, they'll just send out the inside and that'll be it done. And you'll get shuffled backwards quickly.
"But equally, if you put up too much of a fight, you can dig a huge hole for yourself and whoever you're fighting and then you'll get swallowed up by three or four other cars as well.
"I tried to keep it fair, tried to be firm, obvious and clear with my moves to defend. I mean, Mitch going around the outside of me into Turn 6 and I even came over the radio like, 'fair play, he got me there!'.
"He took a risk and it paid off, so well done to him - but I thought out there it was all pretty decent, hard racing but fair.
"Bit weird when Nyck went down the inside and hit the bump, and locked up into Turn 6. That was sketchy, but otherwise, all right."
The 12 points Sims scored in New York has elevated Mahindra to eighth in the championship on 25 points, three ahead of Nissan in the standings.
Mahindra's previous best result of the season was a seventh-place finish achieved by Oliver Rowland in Berlin.