Ross County manager Derek Adams was left "bitterly disappointed" by goals scored by Inverness in their Scottish Cup fourth round tie.
Philip Roberts scored with the last kick of the ball to level the game.
And Adams insisted two bad decisions had led to goals which cost his side.
"We're obviously bitterly disappointed," he said. "Inverness's second goal was offside and there was two minutes of injury time and they scored in the 93rd minute."
"We deserve to be in the next round of the Cup."
Adams felt his side had upped their game significantly after the break, and dominated the second half.
"We were the better side in the second half and created more of the opportunities," he said.
"We needed to be better than the first half, the first half we didn't do well enough. We didn't cause Inverness enough trouble."
However, he conceded that his side would go into the replay on Tuesday 11 December as underdogs.
"Inverness will go in there as favourites with it being in Inverness," said Adams.
"We'll go there and try and do as well as we did in the second half."
Billy McKay had volleyed the visitors ahead on the half-hour, only for Rocco Quinn to equalise with a splendid shot four minutes into the second half.
A deflection off Richie Foran put Caley back in front with 16 minutes to go but County were level again when Iain Vigurs netted on 85 minutes.
A Richard Brittain free-kick put the home side ahead for the first time in the second minute of added time before Roberts knocked in a dramatic late, late leveller.
Caley Thistle boss Terry Butcher said: "It wasn't the same quality as the first game (Inverness won 3-1 when the teams met in the league on 5 October) but there was still plenty of action and incidents.
"We are just delighted to get them back to our place. I'm really happy with that, considering we lost a goal in added time.
"It was good to go in at half-time in the lead. But they equalised quite quickly in the second half.
"To be fair to Ross County, they really had a go in the second half. They pinned us back and got the ball forward quickly. They dealt with the scraps and the second balls better than us.
"But then we scored and you are thinking with seven or eight minutes to go we can grind this one out. But then, disappointingly, we concede two goals but we had to character to come back and get the equaliser."
"I said to the players afterwards you never know when you're beaten. If you have that resilience and toughness in your team it's going to be a cracking season."