Daizen Maeda opened the scoring for the visitors in the fifth minute but the Light Blues fought back through a Ryan Kent strike and a James Tavernier penalty after the break.
However, Kyogo Furuhashi equalised in the 87th minute to preserve the Hoops' commanding lead in the title race.
It was the first time in five games that former Rangers assistant coach Beale had failed to land all three points since returning to the club from QPR and he spoke about regrets - such as Malik Tillman's blocked shot at 2-1 and the two conceded goals - while analysing title hopes.
He said: "In the big games, it is big moments, isn't it? I am sure there will be a little bit of regret on both goals - more than a little bit of regret.
"We should do better. We are the home team and, as a group, when I worked with them previously, they pride themselves on clean sheets. That is the third time we have let in two goals, so we are going to have to improve on that.
"Certainly in big games at home, I am not sure we are going to be able to let in two goals, and not two the way that we did.
"That might seem harsh on the team but that is the reality. We did a lot of good things. We are no further away than we were five games ago.
"The points are the same. There's 18 games to play. It is Celtic's to throw away in terms of the league but in terms of our mentality and where we are, I think we are one or two steps ahead than we were a few weeks ago but we need to be 10 more.
"I thought in terms of where we are at, that's the best performance since I came here.
"We were very unfortunate not to win the game. I wouldn't say we were clearly the better team so a draw to some people's eyes might be fair also."