Scotland's 3-2 defeat by the Czech Republic in Prague, after they led 2-0 with 25 minutes remaining, confirmed the victors' place in the Netherlands and Belgium. Brown's men, meanwhile, reconvene in the autumn locked in a four-way fight with Lithuania, Bosnia and Estonia for the runners-up spot.
"A long, hard season took its toll on us in the last half-hour," the Scotland manager said. "But if we can get back to somewhere near full strength I can see us winning our remaining four fixtures and making the play-offs.
"No one could accuse us of being boring, though it would be nice to get back to being solid at the back. It's been disappointing to concede goals in recent games, especially from set-pieces."
Brown has not given up hope of staging the home match with Bosnia in October rather than in mid-August, as Uefa has ordered. Looking further ahead, he welcomed Dalglish's return and the possibility that his impact might extend beyond Parkhead.
"I hope that there's a spin-off for Scotland," Brown said. "Kenny has always shown true patriotism. Even when he was winning his 100th cap he was incredibly enthusiastic. I'm sure his appointment will prompt Celtic to sign the best Scottish players and run a productive youth policy."
As for the Czechs, who have now won all seven group matches, the evidence of two games against Scotland threw out confusing signals as to their prospects of repeating the run that swept them to the final of Euro 96.
Any side who can come from two down late in the game are clearly not lacking in spirit. There are also pockets of world-class ability, manifested most obviously against Scotland by the Lazio midfielder, Pavel Nedved, and in patches by Patrik Berger and Vladimir Smicer.
But then there is Karel Poborsky. Now with Benfica and approaching 50 caps, he still has only one goal for his country, the one against Portugal at Villa Park which sealed his move to Manchester United.
Despite the fact that the Czechs used two enormous strikers, Vratislav Lokvenc and Jan Koller, who are to international football what Kevin Francis is to the English lower divisions, Poborsky's service from the right wing was at best fitful.
Another player well known to Premiership audiences, the goalkeeper Pavel Srnicek, retains a weakness on high balls which played a part in Scotland's opening goal, a Paul Ritchie header.
Surprisingly, Jozef Chovanec can find no place in his starting line-up for the Nuremberg striker, Pavel Kuka, whose high-quality equaliser within minutes of being sent on took his international tally to 25. Although Scotland were ultimately undone by a Koller header after the Czechs resorted to route one, Kuka's cleverness is likely to be the more viable option in more exalted company.
n Uefa, European football's ruling body, is to ask the Danish football association why fewer than 250 fans from Denmark watched Wednesday's Euro 2000 qualifier against Wales at Anfield. The Danes, who won 2-0, had vetoed switching the fixture to Ninian Park, Cardiff, because of the latter's limited capacity. They claimed 4,000 of their fans would go to the match.