Scotland’s hopes of qualifying for Euro 2016 were ended on Thursday night when they were pegged back to 2-2 by Poland at Hampden Park in the final seconds, coupled with the Republic of Ireland’s 1-0 win over Germany.
Strachan’s contract expires at the end of the qualifying campaign, leaving his future unclear but he refused to address that topic after the match, such was his disappointment.
However, former Scotland forward Dalglish is in no doubt that Strachan should continue.
“I think you are off your head if you think you are going to get anybody better,” Dalglish said in Glasgow, where he was helping officially open Dalmarnock Legacy hub.
“It’s always the manager that gets it, isn’t it? But why change the manager if you can’t get a better one and you won’t get a better one?”
Dalglish, who won a record 102 caps for Scotland, added: “I know there will be disappointment that we’ve not got there but we gave ourselves a great chance.
“It was a difficult group to get out of, so the disappointment should be overruled by a bit of common sense.
“I think the effort they put in was fantastic when you consider who they were up against.
“The game they lost in Georgia, in the end, proved to be quite important but one bad game out of eight or nine isn’t too bad and I think they can be proud of what they tried to achieve.”
Strachan will be hurting more than anyone according to former Scotland boss Alex McLeish.
Poland skipper Robert Lewandowski’s last-gasp equaliser at Hampden, after superb goals from Matt Ritchie and Steven Fletcher had overturned the Bayern Munich striker’s third-minute opener, left Scotland still looking for a first major tournament appearance since 1998.
McLeish’s Scotland side missed out on Euro 2008 with a 2-1 defeat to Italy in the final qualifier at Hampden thanks to Christian Panucci’s stoppage-time goal, and knows exactly how his ex-Aberdeen and Scotland team-mate is feeling.
“He is passionate, he cares and he is a winner,” he told Press Association Sport.
“He was won things all his career and he will be really hurt. There is nobody who puts more pressure on the manager or coach than himself.
“He is conscientious. I am a conscientious kind of guy, I took it personally, and he will take it personally.
“It was a victory snatched from us last night.
“We lost an early goal when I was in charge in the Italy game. It leaves you with quite an attempt to get back into it but they fought back as Scotland typically do and it was a good performance.”
McLeish believes Strachan should stay on as boss on the basis that “by and large he has got the best out of everybody.”
However, he acknowledged the obvious conclusion that results were still not good enough to break a depressing run of qualification failures.
“I think he should stay,” said the former Scotland defender.
“In my opinion he is suited to the role. He has done a good job and he has done what a manager should be doing which is getting the best out of them all.
“But it is up to Gordon. The last thing he would be wanting is for former team-mates and ex-managers coming out and saying ‘he should do this’ or ‘he should do that’.”
Meanwhile, goalscorer Ritchie “absolutely” wants Strachan to stay for the 2018 World Cup campaign which starts next year.
He said: “It is down to him and the people above to see what happens in the future but absolutely. He has been great since I have come in and I hope things get sorted
“I think continuity is important. Since I have come in the ideas of how we are going to play and the way we approach games has been very much the same and I think that is important.”