Dundee brought a run of five successive home league defeats to an end with a draw against Hearts, who opened the scoring after just two minutes through Ross Callachan.
McCann’s side responded with an equaliser from Sofien Moussa just before the half-hour mark and should probably have secured all three points on chances created.
Now Dundee, who are four points clear of 11th-placed Partick Thistle and have a superior goal difference, must visit Celtic and Rangers in the space of four days before the split.
“Listen, it’s going to be a big, big task to go to Glasgow twice in succession,” said McCann, who has appealed a two-match touchline ban imposed last week for a fracas after the final whistle in a 4-0 loss to St Johnstone last month.
“It’s also a big demand on the fans to dip into their pocket for that but hopefully they will have seen enough from us today to see that it’s doable because we need their support.
“The biggest thing for me is that when we are on it we can go to Glasgow and cause Celtic and Rangers problems – if at our best.”
Dundee still need points to feel safer at the bottom. They haven’t won at either Celtic Park or Ibrox since triumphs at both grounds in the same season and within the space of a few weeks in 2000-01.
“I am disappointed a wee bit that we didn’t get three points because I think we probably deserved them,” said McCann.
“I am looking for that [show of character] from the start of the season. But I do believe we have shown enough throughout the season to show that we are a very good side and I said that to the guys before the game.
“We proved today that we were on it and were a tough side to handle.”
Craig Levein felt frustrated at being unable to hail the victory that would have secured Hearts a top-six place.
Motherwell can still overhaul them if they win their next two games by sufficient margins, against Aberdeen and St Johnstone, and Hearts fail to take anything from this weekend’s home clash with Aberdeen.
“It’s not quite secure yet,” said Levein. “I had hoped we’d get three points and then that would be it finally put to bed. We will just have to do what we’ve got to do next week against Aberdeen.”
The manager pointed to a miss by Kyle Lafferty after 26 minutes in yesterday’s clash as a turning point. Already one up, Hearts could have taken a commanding lead but Lafferty saw his shot saved by Elliott Parish.
“The biggest moment for me was at 1-0 up,” he said. “Kyle had a fantastic chance but the keeper made a great save then Dundee went up the park and got the goal just after it.
“So the frustration was that we could have gone 2-0 up and then it would have been much more difficult for Dundee to come back.
“Coming up here is not the easiest of places to win. I didn’t think we did enough to win the match, but you can say the same for Dundee.
Hearts had to push 16-year-old defender Chris Hamilton on to the bench after Connor Randall fell ill before kick-off. “We finished with five academy players on the pitch and that’s obviously the route we’re going down,” said Levein.
“I thought they acquitted themselves well today.
“Young Harry [Cochrane] has played a lot of matches. He played three games with Scotland Under-17s which obviously wasn’t great for us so I was just a bit careful about pushing him too hard, which is why he didn’t start today.”