Cliff Byrne was shown a straight red just nine minutes into the match when he hauled won Jeremie Aliadiere as he chased a poorly-cushioned header from the Iron defender Rob Jones.
Adam Johnson, the winger who had scored twice in Boro's 2-0 win at Glanford Park earlier in the season, converted the penalty to give the home side the lead.
"Things go against you and you have to dealt with it, when you lose a man early on it is disappointing but we are not looking for any excuses," said Adkins.
"We were up against it after nine minutes but that's life. You have to adapt and deal with it.
"Despite that we worked hard and there were some good displays. Grant McCann and Garry Thompson did well and caused them some problems in the second half but they are a good side and it was always going to be difficult here even with 11 men.
"We are a footballing side and we try to be adventurous and that's been our undoing at times. But we have to try and learn. No one goes out to make mistakes. We have to analyse it and improve."
United never looked like getting back into the game, with Rhys Wiliams and Aliadere scoring to seala comfortable 3-0 win for the Teesiders.
The victory was a relief for Gordon Strachan, the Boro manager whose side had not win a home game since replacing Gareth Southgate in October.
"We played at tempo and created a few good chances even before they went down to ten men. And after that we created quite a few more," he said.
Boro were also reduced to 10 men in the closing stages when Lita was sent off for violent conduct, after an off-the-ball clash with Andrew Wright.
"Leroy said he had shrugged him away and I presume that makes it violent conduct, but I have looked at the incident again on the tape and I can't see anything," added Strachan.