Hamilton is now five races without a win for only third time over a single season since 2014. Red Bull have won all five of those, with Verstappen triumphing in four.
Damage to his car apparently sustained over a kerb at Turn 10 saw Hamilton fall behind both team-mate Bottas and third-placed McLaren man Lando Norris.
But Wolff, despite describing himself as "a sceptical person, cup is half empty rather than half full", tried to look at the positives.
"First of all, the result looked worse than it was in terms of pace," he told Sky Sports. "We were stuck behind the McLaren.
"In terms of pace, we probably could have been there, maybe not enough to win the race but right there, which is a step forward.
"The damage occurred at Turn 10, over the kerb; I don't think he was particularly running too hard over the kerb – it was just the part that fell away.
"We looked at the loads and they were the same as in the laps before, so we need to find out why that happened.
"So, overall, damage limitation? Maybe. I think we're going to go to Silverstone, blow everybody away, finish one-two, 30 seconds in advance of everyone else."
He added: "We're one DNF away from being right there in the constructors' and in the drivers' championship, so this is far from over."
This was not the result Hamilton – still two victories shy of a landmark 100 – would have wanted to celebrate his new two-year contract.
But Wolff said: "The morale is good, but we have to be working on these feelings actively.
"If you come from a run of seven world championship titles, everything looks like a defeat, whatever result you have. I think this is a switch in mindset we have to achieve now.
"Today we finished second and fourth, it's not the end of the world. You see how happy the McLaren guys are about their position [P3] and I think we have to just recognise this is a tough, tough championship.
"This is the Formula 1® world championship and you can't expect every year to cruise away in the sunset.
"We will make everything that's needed to not make Red Bull do exactly that."
Perhaps Hamilton himself could use a more optimistic outlook, rueing "a lot of damage" despite insisting he "wasn't going over the kerb any more than anyone else".
"There were a lot of points lost today," Hamilton said, adding: "I would have been second. I was in second when all of a sudden it obviously broke.
"It would have been an easy second generally, but obviously not able to catch up with the guys ahead."
A home race for the seven-time champion at Silverstone is up next, but Hamilton said: "We're miles away from [Red Bull], so we've got a lot of work to do.
"We need all hands on deck, which I know there already are. They brought a lot of upgrades, clearly, over these last few races, and we haven't brought any.
"We've got to find as much performance as possible, otherwise this will be the result most often."