The Jambos’ lead at the top of the table was cut to four points as Rangers maintained their title charge with a 3-0 win over Dundee.
But Hearts made sure they kept Celtic six points adrift in the title race after a four-goal thriller at Tynecastle.
“We are a wee bit disappointed that we did not take all three points. Most teams would have been happy with a point against a team like Celtic, but we rattled them today,” said Mcinnes.
“To come back twice tells me everything. For us to be top for four months is not just a purple patch and we want to keep the whole thing going.”
Celtic made the perfect start when Benjamin Nygren’s free-kick arrowed into the top corner.
Hearts were without a number of key players due to injury but battled back in the second period as Stuart Findlay headed in from a corner.
Yang Hyun-jun restored Celtic’s lead after an impressive run and cross by debutant Tomas Cvancara.
But for the second time in four days, Martin O’Neill’s men failed to hold onto a lead after being reduced to 10 men.
Austin Trusty was sent-off after a VAR review for denying a goalscoring opportunity.
“I’ve seen it back and I have to say I don’t see it. Maybe I’ve been out of the game too long or have misread the rules,” said the 73-year-old O’Neill.
“But first of all, the ball that’s played is going away from goal and we have a man round on the cover. It is not a red card. It is gone now, but it played a massive part.”
The visitors resisted until three minutes from time when Claudio Braga hammered in the equaliser.
Rangers cut the gap on Hearts and edged ahead of their Glasgow rivals thanks to an eighth consecutive victory.
Danny Rohl’s men had to wait until after half-time for the breakthrough at Ibrox through James Tavernier’s penalty.
Two more goals in stoppage time from Danilo and Djeidi Gassama added gloss to the scoreline.
“I spoke about being hunter and this is still where we are,” said Rohl.
“We want to be on the front foot. We want to win our games. If you do this, then in the next 15 games there is a big opportunity there.” (AFP)
