Celtic's top scorer Scott McDonald, who started as substitute amid rumours of a bust-up with manager Mowbray, came off the bench in the second half to show his team-mates the way to goal with his 79th-minute header.
However, with the visitors' first real effort on target, Lee McCulloch equalised from a Steven Davis corner two minutes later.
McGarvey said that Celtic simply have to buy a top-class striker and centre-back - even if they have to pay over the odds.
"There is no option for the Celtic board," he said. "They have to bite the bullet and spend big money.
"Celtic need a proven scorer and a proven centre-half and they are going to cost money.
"It's up to the manager to go and ask for that money and I don't mean enough for a £2million striker or defender. He needs a lot of money
"He cannot buy more squad players, there are enough of them at the club at the moment.
"Celtic will have to buy quality players who will start every week and they will cost more than one or two million pounds.
"But what is the alternative? Rangers winning the title again?
"It's not as if problems will disappear," McGarvey continued.
"They keep leaking goals at one end and they don't score enough at the other.
"I was willing to give the team the benefit of the doubt but I can't keep doing that.
"With two good signings Celtic can win the league but if they don't then they will struggle.
"And if they don't buy and fall further behind Rangers then Celtic Park will become like a ghost town, the crowds will plummet further.
"You seen the crowd against Hamilton in the previous game, the stadium was half-full.
"And there can be no excuses, they have to get players in as soon as possible.
"They have had six months to do their homework, they shouldn't be waiting until the final couple of days of the transfer window."
McGarvey, like most Celtic fans, still cannot believe Rangers escaped with a point.
And like many of those same Hoops' supporters, the former Scotland international believes Mowbray blundered by leaving McDonald on the bench at the expense of Marc-Antoine Fortune and Georgios Samaras.
"I don't think I have ever seen a more one-sided Old Firm game, especially in the first half," he said
"It was unbelievable how Celtic could dominate a game like that and not win.
"Rangers were awful, they didn't deserve to take anything from the game.
"I couldn't believe this was a team who had scored 23 goals in their last five games.
"They didn't have a shot on goal or even a cross into the box in the first half.
"But there is no point in playing well and not winning games.
"Not playing McDonald from the start was a mistake. He is the most natural goalscorer at the club and he showed that when he came on.
"Celtic can get rid of Samaras and Fortune, they are not natural scorers, but McDonald must stay.
"He cannot be allowed to leave the club."