Verstappen saw his lead cut at the top of the drivers' championship to 62 points by McLaren's Lando Norris in Monza, with Charles Leclerc also closing the gap.
The Dutchman has now gone five Grand Prix's without a pole position, his worst streak since the sixth race of the 2021 season (five).
He has also failed to emerge victorious in his last six Grand Prix's, with the last time he stood on the top step being at Barcelona in June.
“What’s really impressed me with Max is how he’s really engaged in this process,” said Horner.
“He’s not panicking, he’s working with the engineers, he’s explaining very clearly where the issues are, he’s putting the time and effort in.
“He was in early this morning, he was on Zoom calls last week, he’ll be on the simulator before the next race, and he’s really working hard at this.
"I think he’s shown great maturity as a world champion, the way he’s working with the engineering group.
“Nobody likes the situation we’re in at the moment, nobody’s happy with it and we’ve got to work really hard to turn it around.
"But the one thing this team has is strength and depth in talent, and we’ll come back.”
Red Bull's struggles have also seen their advantage at the top of the constructors' standings evaporate, and are now only eight points clear of McLaren, with Ferrari 39 points off the pace.
But a return to action next weekend at the Azerbaijan Grand Prix offers the team a chance to bridge the gap to those below them.
Only one driver has achieved more than one victory on the streets of Baku, with that man being Verstappen's team-mate, Sergio Perez, who won in 2021 and 2023.
The Mexican has scored the most points on the circuit (100), with only a Lewis Hamilton victory and fastest lap being enough to overtake the Red Bull driver (75).
But Perez has now gone 10 consecutive Grands Prix without finishing in the top five of the standings, the same number of times as in his previous 41 races in Formula 1.
However, Horner is optimistic that solutions can be put in place prior to the upcoming double header of Azerbaijan and Singapore.
“The most important thing is understanding the issue, and I think there are certain fixes that potentially can be introduced, perhaps not the resolve the whole issue but address some of it,” Horner said.
“I think we have a two-week period before Baku and Singapore and then we have another mini-break where we can work in-between Singapore and Austin, so this time now is crucial.”
Looking to cut the gap to drivers' championship leader Max Verstappen, Norris entered the race as favourite after qualifying fastest, only to be overtaken by team-mate Piastri on the opening lap.
Leclerc started from fourth but quickly found himself battling the McLarens for the lead after Mercedes' George Russell locked up on the opening lap, and the Monegasque sent the home fans into raptures by passing Norris at the second chicane.
Norris later undertook Leclerc to once more give McLaren hope of a one-two, with team engineers encouraging the two team-mates to race one another cleanly for victory.
However, Leclerc's one-stop strategy paid off as the McLaren drivers pitted for a second time, and he held off a late push from Piastri to triumph by 2.6 seconds.
It is Leclerc's second victory at the Italian Grand Prix, which he also won in 2019, and team-mate Carlos Sainz held off future Ferrari driver Lewis Hamilton to finish fourth.
There was yet more disappointment for Verstappen, who saw his lead in the standings cut to 62 points as he finished sixth, ahead of Russell and fellow Red Bull driver Sergio Perez.
Data Debrief: Tifosi celebrate landmark triumph
Leclerc's victory was Ferrari's 20th at the Italian Grand Prix, just the second instance of a team reaching that figure at a single venue in Formula One.
The Scuderia previously achieved that feat themselves in Germany, where they have won 21 times.
Leclerc now holds a 20-point lead over Piastri in the drivers' standings, sitting third behind title contenders Verstappen and Norris.
Top 10
1. Charles Leclerc (Ferrari)
2. Oscar Piastri (McLaren)
3. Lando Norris (McLaren)
4. Carlos Sainz (Ferrari)
5. Lewis Hamilton (Mercedes)
6. Max Verstappen (Red Bull)
7. George Russell (Mercedes)
8. Sergio Perez (Red Bull)
9. Alex Albon (Williams)
10. Kevin Magnussen (Haas)
Leclerc started at the front of the grid in Baku for the fourth time in a row, having also claimed a memorable triumph for Ferrari at their home circuit of Monza last time out.
However, Piastri passed Leclerc on a straight on the 20th lap, and a spirited fightback was not enough for the Monegasque driver as the McLaren held on for his second win of the year.
The result means Leclerc remains third in the drivers' championship standings with 235 points, behind Max Verstappen (313) and Lando Norris (254), while Ferrari remain third in the constructors' table.
Speaking about his battle with Piastri after the race, Leclerc said: "It is enjoyable when you've got many opportunities every lap.
"I think maybe McLaren had less downforce and in the straights they were very quick, in the corners we were a bit quicker.
"I couldn't get as close as I wanted and eventually we lost the race when I didn't defend as well as I could have at the end of the straight. Sometimes you make mistakes and I'll learn from it."
Asked at what stage he realised victory was unlikely, Leclerc said: "I think as soon as we put the hard tyres on. On the medium we were very competitive, and the car felt good.
"Unfortunately for me, we didn't do any high fuel running in FP1 and FP2. We went for a setup direction which in the race was a bit more difficult to manage.
"McLaren and Oscar have done an exceptional job and done better than us."
Ferrari team-mate Carlos Sainz, meanwhile, was pushing for a podium finish when he crashed with Baku specialist Sergio Perez, taking both drivers out of the race.
"It's a huge shame for Carlos on the last laps," Leclerc said. "Hopefully everyone is okay, and obviously it's not a great day for the team."
Leclerc edged out McLaren duo Oscar Piastri and Lando Norris for a spectacular win at Monza, racing from fourth on the grid to repeat his 2019 triumph at the venue.
Only Michael Schumacher (five) has won the Italian Grand Prix while driving for Ferrari on more occasions, with Leclerc's second victory drawing him level with Rubens Barrichello, Phil Hill, Alberto Ascari and Clay Regazzoni.
Sunday's win came after Leclerc claimed a home victory at the Monaco Grand Prix in May, ensuring 2024 will be a season that lives long in the memory for the Scuderia driver.
"It is an incredible feeling," he said after the podium celebrations.
"I thought the second time, if there was a second time, would not feel as special as the first, but the emotions over the last few laps were the same as in 2019.
"I want to win Monza and Monaco every year and I have managed to do so. It is so, so special."
Sitting third in the drivers' championship standings, Leclerc now has a 20-point lead over fourth-placed Piastri and is just 23 points adrift of Norris, who has been tipped to push Max Verstappen for the title.
Asked if Ferrari can continue to battle for victories in the closing stages of the season, he said: "I don't know.
"Our package was working well on a track like Monza but whether it will be the same for the rest of the season, I doubt it.
"I still think McLaren are favourites but we have done a step forwards, that's for sure. Baku is a pretty nice track for me, so maybe we can achieve something special there."
