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Dundee eventually chose Queen of the South's Gordon Chisholm to succeed the sacked Jocky Scott as manager.
McCall said: "Dundee fell well short of that figure and, at that point, they looked elsewhere for a new manager.
"Ultimately, it came as something of a relief not to have to make a decision that I might not have wanted to take."
Scott had been sacked on Saturday, despite his side leading the First Division, after Dundee's 3-0 defeat away to bottom side Airdrie United.
"On Saturday, after our match with Morton, and our programme editor will verify this as he was there at the time, I took a phone call from Dundee Football Club," McCall told his club website.
"They also spoke with my agent and again with myself. The upshot of which was that they made it clear that they wanted me to become their new manager.
"I immediately then spoke to our Chairman, Allan Cowan, as there is absolutely no way I would have simply resigned as Thistle manager.
"There is a clause in my contract that allows me to leave Thistle if a certain level of compensation is agreed upon and negotiations between the two clubs did take place."
Saturday's 1-0 defeat by relegation-threatened Morton all but ended Thistle's own promotion hopes and they now lie 11 points behind Dundee.
McCall, though, insisted that his departure from Firhill to the club's First Division rivals was not a foregone conclusion had compensation been agreed.
"As our programme editor will again confirm, I was in absolute turmoil when I became aware of Dundee's interest and was so for the rest of Saturday and Sunday," he said.
"I do have a family to think of, but it would have taken something ridiculous, and it never got that far, to get me to leave Partick Thistle.
"I've developed a real bond for Thistle and the people at the club. This is a club that I think suits my personality perfectly and one that I am proud to be part of.
"I'm anxious for people to realise that, although I have lived a large part of my life in the west end of Glasgow and that my son goes to school locally, being manager of Partick Thistle is not the easy option for me.
"My drive and ambition hasn't been blunted at all. Being manager of Partick Thistle is a tough job, but I've said from the moment I came here that I wanted to do something at Firhill that people would remember for some time and that ambition hasn't changed any."
Thistle earlier this month sacked former Gretna and Morton manager David Irons, citing financial reasons, just seven weeks after he became McCall's assistant following the departure of Gerry Britton.
"There have been some difficult decisions made recently for which I don't blame the board of directors," added McCall.
"Indeed, I believe that we have an excellent board at Firhill and the next two years could be challenging years for the club, though, with most clubs going to be forced to cut their cloth we will be far from unique in that respect."
BBC SPORT