"I'd ridden hard for five laps and on that last lap I just pushed and pushed, giving it everything I could and I'm just pleased I was able to nick the podium back," he added.
"I'm so proud to wear the Joey Dunlop colours from 2000. I was in the same position on the podium with him in the Superbike race that year, and now here I am next to another Dunlop.
"I wanted to win but it wasn't be. I'm on the podium and the consolation is the lap record."
Tyco Suzuki's Martin finished fourth, with Conor Cummins on the Milwaukee Yamaha and Michael Rutter on a third Honda Legends machine completing the top six.
James Hillier (Quattro Plant Kawasaki), Bruce Anstey (HM Plant/Padgett's Honda), William Dunlop (Milwaukee Yamaha) and Josh Brookes on the Tyco Suzuki were the top ten.
British Superbike Championship star Brookes became the fastest ever newcomer in TT history as the Australian lapped the 37.73-mile course at 127.726mph on his final lap to break Steve Plater's previous record of 125mph.
Lincolnshire's Gary Johnson had been in contention for a rostrum finish until his Honda Fireblade ran out of fuel at the end of the second lap.
The Superbike TT had been postponed by a day to allow the Superbike riders additional qualifying time after practice week was hit by poor weather.