Hibbert was handed his first Premier League start in 666 days, with regular right-back Seamus Coleman sidelined by a head injury.
The 33-year-old's display in a 1-1 draw - secured by Phil Jagielka's stunning late equaliser - encouraged Martinez.
Everton's manager was also thrilled by the impact made by 20-year-old Browning, who made his Premier League debut as a replacement for Hibbert with 17 minutes remaining.
Analysing the performances of both players, Martinez said: "Tony played in the Capital One Cup [last Tuesday's 3-0 defeat at Swansea City] and he played 90 minutes and it is obviously a matter of [him] having the match fitness.
"I think we needed his experience. We had Seamus Coleman with a late fitness test until the last second and it was just the right opportunity for him [Hibbert] to bring a bit of understanding, a bit of know how.
"Once he ran out of steam, Tyias Browning in his full debut, he showed an incredible composure, great pace, phenomenal defending and I thought he gave us real penetration down that side.
"Between them, Tony Hibbert and Tyias Browning did a terrific job for us."
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