Huddersfield twice took the lead, through Adam Hammill and Nahki Wells, only for the visitors to equalise twice through Albert Adomah in front of 11,999 fans.
The draw left both sides still looking at the wrong end of the table and visiting boss Aitor Karanka praising the work rate and the finishing of Adomah.
Huddersfield were ahead in the third minute through Hammill with a finish from the left side of the area before Adomah punished a poor back pass from Oscar Gobern.
Wells hit a fine curled effort just after the half hour but Adomah ensured his side a share of the spoils when he fired past Alex Smithies shortly after the break.
Robins was honest in his assessment when he said: "Another day in the football factory and a few more mistakes."
Robins had seen his side gift Blackburn goals in a recent 4-2 defeat and his side were again punished by Middlesbrough.
"It's one of those things you can't legislate for," he added. "We've got to expect them making mistakes.
"When we give them (Huddersfield's opponents) a chance we really give them a chance.
"I thought the game generally was a decent game of football and we've just gifted them two goals.
"All season I have said we have got to take the mistakes on the chin."
Robins defended his decision to take off Wells and bring on James Vaughan with a little over 10 minutes remaining, a move which drew boos from the home fans.
"I knew that reaction was coming but I knew it was the right thing to do," he said.
Karanka was happy to see his side take a point.
"I think the score is fair," he said.
"In the second half we started 100 per cent opposite (to the first), we started very well.
"I am happy today. Not with the first half because we went into the game very, very bad."
Karanka was full of praise for Adomah whose finishing earned the visitors a point.
"I am very happy with him because he was not so good the last two or three weeks. Today he showed me what a good player he is," added the Spaniard.
"He is a player who works 100 per cent. He needed to be confident like today. He is one of our players who we need to score goals.
"We need his goals and I told him that and he showed all his team-mates that he is a leader."
Huddersfield got off to the perfect start when Hammill shot in from the left edge of the area after the home side had won the ball in midfield in the third minute.
Oliver Norwood fed Hammill who finished coolly past Dimi Konstantopoulos for his fourth league goal of the season.
Middlesbrough were level after 10 minutes when a back pass from Gobern set up Adomah and he rounded Smithies before slotting the ball into the empty net.
Wells put Huddersfield back in front with a fine finish in the 34th minute.
The January signing from Bradford cut in front the right and curled a left-footed shot form the corner of the area over the despairing dive of the keeper and in off the far post.
Huddersfield had started the first half well but it was Middlesbrough who matched their opening in the second period to restore parity for a second time.
Huddersfield were punished for losing the ball in midfield and it was once again Adomah who made them pay, this time in the 47th minute.
He claimed possession and hit a fine rising shot past Smithies to again draw his side level.
Huddersfield pushed for a third goal their dominance probably just about deserved but had to settle for a share of the points.