De Gea kept his place despite an error-ridden performance in their FA Cup semifinal defeat to Chelsea on Sunday.
And Solskjaer was happy with the performance, stating: "I knew David [De Gea] was going to be focused. Everyone knows we lost the game on Sunday and our pride is hurt. Every time we lose a game, we want to go out as soon as we can and David is the same. He showed today he keeps his concentration."
With Leicester City waiting for Sunday's finale, Solskjaer remains bullish of a top four finish.
He added: "When we started after lockdown, we had to go for it. We had to go for it for goal difference and had to go for it with points. The effort has been fantastic, the results have been fantastic. Of course, we'd liked to have won against Southampton - when you concede in the last second and here today we've conceded at the end of the first half, but we've given ourselves a fantastic opportunity on Sunday."