The Birmingham-based 24-year-old's personal best is 2.36m, a bigger height that the 2.33m managed by American silver medallist Erik Kynard in the Olympic Stadium.
European champion Grabarz, who last year was outside of the top 40 and had his lottery funding cut, twice clipped the bar with his heels at the height Kynard cleared, and was forced to settle for bronze alongside Canadian Derek Drouin and Qatar's Mutaz Essa Barshim. Russia's Ivan Ukhov won gold with a clearance of 2.38m.
While that made the gold out of reach for Enfield-born Grabarz, on form he knows he could have moved up a step on the podium.
"I won an Olympic medal in front of my home crowd and not a lot of people get the opportunity to do that, and I did it," he said.
"It was really, really enjoyable and I had an absolutely great time. The pressure has increased, especially as in the public's eye I've come from nowhere and all of a sudden people were telling me I'm a medal favourite. To try and live with that is not easy.
"To be able to perform up to those expectations was something to be really proud of.
"There was an opportunity for me to grab silver, but the Games are the Games.
"It's really difficult to perform at a Championships. The reigning Olympic champion and the reigning world champion were not even in contention for medals so that proves how difficult it is."
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- Mutaz Essa Barshim