Goals from Andriy Yarmalenko and Aaron Cresswell left the Reds boss under pressure with his side now winless on the road in the Premier League since February.
Jose Mourinho, whose United team lost at the London Stadium 12 months ago, said: “We were bad last season but I don’t see any improvements this season, even with three new players.
“Im not surprised by the result and I don’t think Ole can take any positives from the game.”
Solsjkaer said: “He’s got his right to his own opinion. Of course we lost here last year – its always a difficult ground to go to and we hoped to do better than we did.
“We hoped for better. But the key moments they grasped and we didn’t. They had two fantastic finishes from two left feet, we just didn’t take the chances when we had them.”
Speaking to Sky Sports, Roy Keane was scathing. He said: “I don’t know where to start. I knew they weren’t in a great place but I am shocked and saddened by how bad they are.
“You can lose a game of football but everything about United was lacklustre. No quality. A lack of desire. A lack of leaders. A lack of characters. It’s a long way back from united and its scary just how far they have fallen.”
United have won just two of their opening six Premier League games of the campaign and host Arsenal next Monday.
They could be without Marcus Rashford who – after five games without a goal in open play – failed to register a shot before going off injured after an hour.
Solskjaer said: “We have to scan him. He felt his groin, he will probably be out for a little while.”
Gary Neville told Sky Sports: “Man United look depleted and defeated. The squad is depleted and the away stand towards the end was depleted. I can’t blame them.
“The coaches that have come in have been given money over last seven, eight years but they’ve been let go when they need another year.
“Ole needs another three or four windows to get this squad up to the standard and a couple £100m to do so. You can bring through young players but you need that spine.”