First Charlie Miller went through one-on-one with goalkeeper Daniel Andersson but could only fire the ball off the Swede's legs.
Then, minutes later, Billy Dodds and Jim McIntyre both had chances to score but were thwarted by Mathias Doumbe - who raced in to clear the ball off the line.
Fifth place in the Bank of Scotland Premier League table was the reward for whoever gained the three points, but both teams cancelled each other out with their desire not to lose.
McCall praised the contribution of Miller and hailed him as one of Scotland's best midfielders, but admitted that the atmosphere in the Tannadice dressing room was flat after gaining only a point.
"Hibs started strongly, but we managed to come back and played some great stuff at times," said McCall.
"We had two great chances in the second half and should have taken them but I can't criticise Charlie Miller.
"The way he played tonight shows how good a player he is and on that form he's as good as anyone in this country.
"We had two penalty claims and I though the first one was definitely a penalty, but the referee told us that Charlie had been too honest.
"That's the way it works in this game and I have to say that although we're delighted to be in the top six, it feels like a defeat at the moment."
Hibs boss Bobby Williamson was happy to get the point and hailed the contribution of his goalkeeper in the 0-0 draw.
He raced from his goal and bravely dived at the feet of Miller to prevent the former Rangers man from scoring.
The Swede also turned in a commanding performance and marshalled his defence well throughout.
"I'm happy with a point, but we could have won the game towards the end," said Williamson.
"Tam [McManus] went close and maybe should have scored, but after the chances they had a draw was probably about right.
"Our goalkeeper did well and made a few crucial saves, especially to deny Miller then Dodds.
"We had a hard night last week and you could see the players' energy sapping as the game wore on, so we're happy to win the point and get into the top half."
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