United is in 10th place with just nine points, its worst start after seven games for 30 years, and it has won just one of its last six league games, Reuters reported.
But with youngsters introduced to the side this season, Irishman Keane, who won seven Premier League titles with United, believes his former teammate needs time to shape the team.
“I think he has been brilliant, a good honest guy. It is hard work at the moment, but there are six or seven young players learning their way,” Keane said on Sky Sports.
“We’re all very impatient, we want success yesterday, but you have to give the man time. He is frustrated, under pressure, but dealing with it. He’s a classy guy but no doubt he will be disappointed at not winning enough games,” he added.
United beat Chelsea 4-0 in its opening game but its only league victory since was a 1-0 win over Leicester City. Keane said Solskjaer deserved the chance to bring in new players.
“They have given him the job. Support him in a couple of transfer windows. Are there more tough days ahead? You bet your life, but you need to stick with it,” he said.
“There was a lack of quality from both teams tonight. Their lack of goals, the lack of opportunities they’re creating.”
Solskjaer said that despite some encouraging individual displays, United’s results were a concern.
“There are many things we look at and many things that give me loads of confidence,” he said.
“We can talk about performances but it’s the results that matter. You can talk about the results, I can talk about the six out of seven games good performances,” he said.