The forward insisted the team was the most important thing despite adding to his collection of personal records
It moved the Juventus superstar ahead of Robbie Keane, who netted 23 goals in European qualifying during his international career for the Republic of Ireland.
It took his international tally to 93 goals, further strengthening his position as Europe's all-time leading international scorer, with footballing great Ferenc Puskas nine behind.
It was also Ronaldo's eighth international hat-trick for the reigning European champions and Nations League winners.
Despite his personal achievements Ronaldo insisted he was simply happy for his team after the huge win lifted second-placed Portugal onto eight points.
"I'm having a good time, but the team was doing very well too," the 34-year-old told reporters.
"I am happy and enjoying this moment, not because I scored the goals, but because of the level we have been able to demonstrate in recent years.
"It is up to me to continue helping the national team."
After back-to-back draws to start their campaign, Portugal have now recorded much-needed wins over Serbia and Lithuania this week.
And Ronaldo feels Portugal – in second spot and holding a game in hand – are now closing in on a place at next year's showpiece tournament.
"The hardest thing was winning in Serbia, and it was important to continue with a triumph here," added the forward.
"We are closer, we have two games – one at home and one away – and I think if we win one of those matches it's enough."