Grealish should have turned home Trezeguet's deflected shot shortly before Lindelof's header put United ahead.
Villa eventually equalised through Tyrone Mings to secure a draw, but Smith says Grealish will still lament his poor miss.
He told Sky Sports: "I wasn't disappointed with the performance, just the manner of their first goal. Marcus Rashford has a header from six yards from a short corner and we've seen it done before so we didn't do our jobs in the penalty box. The first half performance was good, we pressed when we needed to and used the ball very well.
"Second half, they started better, they won a few duels which got the crowd on their side and we had to show rearguard action which we did every well. Not sure we could do more for the second goal, and it's funny how football works. Jack Grealish missed a chance just before that. We didn't have long to wait for the equaliser.
"He knows more than anybody that nine times out of 10 he scores that. He'll be pleased because of his goal but he won't sleep because of that miss."