Stewart Downing says Boro will take Saturday's draw against Burnley as a point gained with seven games remaining to achieve Premier League survival.
Although Boro couldn't take advantage of a number of late chances to grab a first league win of 2017, Downing says Steve Agnew's side will take encouragement from the performance.
"We 100% believe we can survive," he said. "We got a point and the other teams just above us lost so we are a point closer.
"I know we could have done with all three points - and we tried to get them.
"But there's a long way to go yet, and a lot of twists and turns to come."
Downing was involved in some of Boro's best moments in the match, seeing his whipped free-kick cleared off the line by the retreating Matt Lowton, as well as providing the cross for an overhead kick from Alvaro Negredo which was superbly by Burnley captain Tom Heaton.
"I think on chances created, we deserved to win," Downing said.
"Their keeper is probably man of the match today with his saves, which says everything.
"They are well drilled, well organised and hard to break down, but we were passing well, pushing it around and putting a lot of balls into the box.
"The pleasing thing is that we're creating chances, we just need that break and a little bit of luck for one to go in."
Downing praised the Boro fans, adding that their support will be vital with the likes of Arsenal and Manchester City to visit the Riverside in the season's run-in.
"The fans stuck with us," he said.
"They were very good. That's the support we need. We need the fans behind us and we'll get that win that will kick us on."
"We've got some big teams to play yet so it will be tough, we know that. But do they fancy coming here? We'll soon find out.
"We tend to play well against the top teams and I'm looking forward to it. It's a big challenge.
"We know what we need to do, and we will carry on. The positives from that we take into the Arsenal game."