Boro took the lead through an own goal from former player Sean St Ledger and then missed a golden chance to add another in first-half stoppage time when Marvin Emnes got free in the box but failed to slot home, before Grant Leadbitter lashed in a shot that was well saved by Kasper Schmeichel.
The Foxes came roaring back after the interval with goals from Danny Drinkwater and Jamie Vardy, and they could easily have had more in a second 45 minutes that was a reverse of the first.
And Mowbray admits those near-misses before the break swung the match in Leicester's favour.
"You have to say that the chance for Emnes just before the break was pivotal," said the Boro boss.
"If we could have got 2-0 up at that stage then it would have been a long way back for Leicester on a hot day. We didn't and we are very, very disappointed with that.
"But the bottom line is that you have to take those chances. We said it so many times last season that you have to close out games when you are are on top.
"We played really well in the first half I thought. We had a good shape, we passed the ball around well and we created chances. We made good decisions in key areas.
"But Leicester are a good side. They came back at us in the second half and we stopped doing the basics well and we let them back into the game."
Leicester boss Nigel Pearson agreed that the game swung dramatically in the second half.
"The momentum in games in the Championship can change very quickly," he said.
"In the first half we didn't work hard enough. I didn't think we made enough positive decisions and we let Middlesbrough shape the game.
"But in the second half we made a few more positive decisions and worked harder and we got our reward. We scored two very good goals, we could have had a few more and possibly we should have had a penalty too.
"We were well worth the win today overall, although it looked a bit precarious at half-time."