After a bad first lap at the season opener in Bahrain, Alonso, who had been strong throughout the weekend, recovered to third having been helped by the retirement of Charles Leclerc.
However, he still finished 38 seconds behind winner Max Verstappen, who was not stretched in the latter part of the race.
Alonso himself believed that with a better start and without the need to fight past other cars he might have been 20 seconds behind, but that doesn't take account of what Red Bull may have had in hand.
"I think the gap is still substantial," said Krack. "We don't know how much management that Red Bull had to do and did.
"I think it was quite comfortable for them to just get the mandatory tyres through and cruise the race to the end. So I think we have now one good result, we have improved our car.
"But we are fighting here with teams that are used to drive on the front, they are very used to high-intensity development. So I think let's be respectful and humble, and see how it continues."
Asked if the team can regularly target podiums he added: "We must not lose the ground under our feet and dream about podiums straight away. We knew that we were not bad. We knew that we had a strong race pace.
"But so many things could go wrong. And after two laps, and I was not dreaming about the podium, to be very honest with you. So you have to just see how the race unfolds and just focus on your job. And we had also the attrition of Charles, which we shouldn't forget.
"So all in all, I think you can dream about podiums. But you should not believe that."
Krack said the team is up to fully exploiting a more competitive car, despite the lack of recent experience fighting at the front.
"We must not forget, we speak here about Team Silverstone," he said. "Team Silverstone is a very experienced team with a lot of fantastic people that have done that already. I think we clearly saw it today, with the race strategy.
"The team did not get carried away by stopping early, by trying to undercut, but by sticking to its plan, and the tyre advantage that was built-in at the end of the day, was I think, instrumental also to help to pass. And so I think we continue to try to do our best there."
Asked about where the AMR23 can be improved, he said: "We need to analyse it first. It was a very intense first weekend, we now have better references than we had before the weekend.
"So I think we need to sit down, analyse properly. Where are our strengths? Where are the weaknesses? And then, as usual, work on the weaknesses.
"We wanted to make a step forward, we did not say we want to beat Red Bull. Let's keep the feet on the ground.
"Let's work hard, because it could be that in Jeddah we may be fourth or fifth or sixth or so, in terms of team ranking. So I think let's enjoy today, and we continue to see how it goes on."
