The club wraps up its Premier League campaign with a fixture against relegated Fulham at Craven Cottage on Sunday.
Dubravka played every minute of every game – 3,240 in total – as Newcastle’s players fought back after failing to win any of their first 10 games.
United are 14th in the table ahead of the Fulham game, and could move up one place if they win and 13th-placed Bournemouth lose to Crystal Palace.
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Asked to reflect on the season, Dubravka said: “It was up and down.
“The first 10 games was really tough for us, especially mentally, because if you don’t win in 10 games, it’s really hard to keep going.”
Dubravka believes that the biggest result of the season came against defending champions Manchester City at St James’s Park in late January.
Newcastle came from behind to win 2-1 thanks to goals from Salomon Rondon and Matt Ritchie.
“A lot of people probably expected that we would keep losing the games, but after that, probably the crucial game was against Manchester City,” said Dubravka.
“That gave us so much confidence, and after that we had the run of victories.
“We were very close also with the big teams and even the away teams, but we are safe, and that’s the most important thing.”
Fulham, meanwhile, were relegated early last month.
Former United midfielder Scott Parker was put in temporary charge in February after the club sacked Claudio Ranieri, who had succeeded Slavisa Jokanovic, dismissed in November.
Dubravka wants Newcastle, beaten 3-2 by Champions League finalists Liverpool last weekend, to end the campaign with one more win.
The goalkeeper said: “We definitely want to win the game. You can see it was a great effort (against Liverpool).
“The fans were incredible. Unfortunately, we lost.”
United twice came from behind against Liverpool, only for Divock Origi to score a winner four minutes from time.
Origi went on to score a dramatic winner against Barcelona at Anfield three days later.
“We’re disappointed,” said 30-year-old Dubravka. “We felt that we could probably take one point. It was up and down, and we felt a draw would be fair, maybe.
“We didn’t put our heads down, and we were trying to be dangerous and we scored two very nice goals. To be honest, they didn’t create too many chances.
“They had probably one more chance in the first half, and that’s it, and then they scored from the set-pieces.
“We gave them a golden opportunity to score. It was not the best from our side, but we showed character, and we were full of emotion.”