The Frenchman, who took his second podium place of 2012 having finished just 2.5s behind winner Lewis Hamilton, used a one-stop strategy to move up from seventh on the grid.
But as he moved ahead of Mark Webber, he didn't realise he was so far up the race order.
"We thought about going for one-stop [before the race] and decided to see what was going on later on. The question was whether to go with the option tyres from the beginning, especially since they had already done two runs in Q2 and Q3," he said.
"But then the car felt pretty good and when we put the prime tyre on, I didn't know what was going on in front of me. I had Nico Rosberg and Mark Webber in front, so I was fighting with them and was pushing quite hard, but I knew that I was trying to go for a one stop and finally when I saw Mark coming in my tyres were still quite fresh.
"I didn't realise I was third and then I saw Fernando [Alonso] was slowing down and I was second. So it was like a crazy end to the race, because I was thinking P4 or P5, but the pace stayed there.
"The team did a fantastic job to give me a car which was good on tyres, we knew with the heat we would be better today and thankfully the sun came and that was fantastic for us."
Grosjean added that he believed that his result was further evidence that Lotus is capable of fighting at the front regularly.
"It means we are in good shape for working with the team and improving every time," he said. "We had a bad Friday with different conditions from today.
"I was sure we could have achieved better, we are working quite well so I am pretty pleased with this podium and it means we are still here after seven races, it shows we are fighting at front and having good results."