An early Ashley Barnes strike and a superb free kick from Steven Defour had put Burnley two goals to the good, but Lingard scored soon after coming on as a half-time substitute and then found the equaliser in stoppage time.
Manchester United manager Jose Mourinho suggested he needs bigger investment from the club if he his to be able to produce the kind of team that will challenge Manchester City for titles.
Even though majority love him, United fans were absolutely furious with Rashford and vented their anger on social media.
United manager Jose Mourinho showed his frustration after a number of decisions by referee Martin Atkinson but his own initial team selection was perhaps a mistake.
"The boys fought against the 2-0 at half-time, so nothing at all negative to say about my players".More news: TZH: Salman Khan film smashes records!
"Now we feel frustrated and angry but we need to keep going and, from tomorrow, rest and think about the next game and have the will of finishing the next game with a much better feeling".
Paul Pogba has five assists to his name despite having played just nine Premier League games, but such ability on the ball makes him a marked man.Lukaku, on the other hand, is a relative unknown in the creativity department.Having created just three big chances all season prior to Saturday, Lukaku proved he can adapt his game to give Mourinho more options. You think Real Madrid are not as big as we are?
Asked if they are in a rough patch, he replied: "Why?" Burnley have seven players injured or suspended for this match, with impacts all over the pitch, including leading scorer Chris Wood. Because the opponent went to our goal twice and they score twice? I talked to the players at half time when it was 1-1 that it was an easy match to win.
Burnley boss Sean Dyche was proud of the way his side defended but was unhappy with the award of a free-kick against Sam Vokes that led to Lingard's leveller. "I was not happy with the result against Leicester", he said. "The game plan is you're going to have to defend and do all of the ugly details of the game well".
Dyche said: "Overall, to come here and get a point is very pleasing, especially when the squad is stretched".
"Yes, and I had the chance to speak with Ashley Young to tell him the way the team had to be in position because of Smalling's difficulty, but I think a lack of maturity because I can not stop the game to give a team-talk for the last two minutes".