Russell and teammate Lewis Hamilton started the race, on medium tyres, second and third on the grid ahead of Red Bulls Sergio Perez, while his teammate Max Verstappen started in pole position both on the soft tyres.
At the start of the race on Lap 1, Russell was passed by Hamilton and Perez dropping to fourth and a bit later both Mercedes cars changed tyres to the hards and Red Bull switched to mediums and Verstappen and Perez we able to make their tyres last until the finish.
This meant that Hamilton and Russell ended up finishing second and fourth overall.
In an interview after the race, Russell admitted to be frustrated by missing out on the podium, and said: "Yeah, it was a little bit frustrating [to miss out on the podium].
"I made a good start, but Lewis was there on the inside and I was probably a little bit too cautious there [with] my teammate. Ultimately that probably cost me two positions today because I would have ended up in second and things would have been different maybe.
"But nevertheless, really happy that we are making a lot of progress as a team. Especially when you look at it compared to Ferrari, [it's] really impressive [the] performance that we are bringing week in, week out," Russell said.
The 24-year-old Russell admitted that Red Bull were still in "a league of their own" but added the Mercedes was a lot closer.
"Red Bull are still in a league of their own, credit to them. Perhaps today if we were on the same strategy as them, we would have been a lot closer, so again a positive to takeaway."
The race strategy by Red Bull, particularly with the soft-medium tyre choices, worked well and Russell said that had been a big factor in their Mexico GP success.
"In hindsight, starting on the softs and going to the medium was the right thing to do. Starting on the medium and going to the softs was a bit more difficult because my medium was already quite damaged from the early couple of laps," Russell said.
"We need to understand why Ferrari and Red Bull opted to start on the softs and we didn't think that was the right thing to do. As I said, I'm really pleased with the progress we are making."