Scotland sit fifth in World Cup Qualifying Group F after 3-0 defeats to England and Slovakia, in addition to a disappointing 1-1 home draw with Lithuania.
Strachan oversaw an underwhelming 1-1 draw with Canada at Easter Road on Wednesday, and next face Slovenia at Hampden Park on Sunday, in a critical tie for their World Cup hopes.
Despite the pressure on Strachan though, Dalglish has backed his former team-mate to turn it around.
"I don't think the SFA were wavering, were they? And I don't think Gordon [Strachan] was wavering," Dalglish said.
"People like to apportion blame, and it's usually the case that the manager is going to cop it, but I don't think anybody could have done a better job than what wee Gordon has done so far.
"Whether he wants to maintain the role was put in question and he certainly poured cold water over the fire for that one. He certainly came out very strongly.
"And by the way it just shows you how passionate he is. There are a lot of people with less guts and less heart that would have maybe walked away, and maybe less belief in the players would have walked away. So good luck to him."
Scotland missed out on a place at Euro 2016 after a qualifying defeat to Georgia, combined with Poland and Republic of Ireland's victories over Germany, which ultimately saw the Scots finish fourth.
England, Wales, Northern Ireland and the Republic all qualified and featured in the knockout stages of that tournament in France while Scotland were forced to watch on, but Dalglish is positive over Scotland's future.
"There's a few Scottish players in recent years that have started playing in the Premier League that we never had before," the former Celtic and Liverpool forward added.
"You go through the teams and there are one or two in there, and that's progress from where we were.
"The more players you have got playing at a high level, the better chance you have got with getting results as a national team.
"It has been disappointing, I think everyone would admit that, and there will be nobody more disappointed than Gordon. But I think it's moving forward. Slowly, but it is moving forward."
