Two goals down at halftime, Lingard came off the bench to rescue the point for United.
"The first one [chance], it just kind of hit me and, nine times out of 10, that would have gone in," he told MUTV. "But it hit the keeper's face, bounced on to the crossbar and bounced out. But after that, we stayed positive and had plenty of players in the box to score goals and I'm glad that we did.
"It was coming behind me [from Young's cross, for the first goal] and it was just instinctive to do that. As soon as that went in, the crowd went up and it gave us that extra buzz to go and get another goal. It dropped to me very quickly [in injury time] and, like you said, it was instinctive again to shoot straight away. If we had played for another five or 10 minutes, we would have won the game."
The manager passed on his half-time instructions to Lingard, who is fast becoming a key figure and now has nine goals for the season in all competitions, with five of them coming in this month alone.
"[The message] was always believe," revealed the England international. "Never give up. We knew we had another 45 minutes to play so we had to be patient, keep moving the ball, moving Burnley about, and eventually we created two clear-cut chances which we scored from.
"This role, further inside, allows me to be closer to the striker, to get in the box, create more things and obviously have more shots at goal. I thought we could nick it towards the end but obviously time ran out and now we look forward to the next game [against Southampton]."
"We always have that fighting spirit, that never-give-up attitude and we'll see where it gets us."