But after feeling unwell and dizzy when he got out of the vehicle, Massa cancelled his post-session media activities and went to the medical centre at the track to see doctors.
"He felt unwell again during FP3 (third practice) and has made the decision to withdraw from the weekend", said the team.
"Williams supports Felipe's decision and the team will work with him to ensure he makes a full recovery, with a view to return to the race track for the Belgian Grand Prix".
Whatever happens to Di Resta in Sunday's Grand Prix, the 2017 Hungarian Grand Prix will not be one he forgets in a hurry.
He drove in 58 Grand Prix for the Silverstone outfit, with a best result of fourth place in the 2012 Singapore Grand Prix and 2013 Bahrain Grand Prix. He was cleared to take part in Saturday's final session before qualifying but ended it early.
Di Resta will not get any practice in the vehicle, owing to Qualifying due to start at 13:00pm United Kingdom time. Brundle is absent from this race after he was taken ill moments before the British Grand Prix a fortnight ago.
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"It's weird. I was sitting talking about what we'd be saying in the qualifying build-up show, but diving straight in, I'm not going to lie, I was scared, I was nervous, anxious".
"I haven't driven one of these cars for 3 and a half years apart from 10 laps I did in a 2014 auto and you get thrown into qualifying which is the deepest of all deep, jumping off a cliff and seeing how you can fight for survival".
"You just have to get in the vehicle and do the best-possible job".
This will be the Di Resta's first experience of Williams' 2017 vehicle, although he did drive their 2014 hybrid at the team's 40th anniversary celebrations at Silverstone in June. There's no pressure out there.
"I think Felipe Massa is more upset than anything else", said Williams.
"You imagine, you're so in tune to doing a race weekend, then at the very last minute to not be able to do it, he's genuinely upset".