"I am the manager of Cardiff City football club and I am not going to lay down and feel sorry for myself," Norwegian Solskjaer, who replaced Malky Mackay as manager in January, told Sky Sports.
"We will go into the next game showing professional pride and put a good effort in, a good performance and then we will plan for next season.
Cardiff will play their final league match at home against Chelsea next Sunday and Solskjaer admitted it will be difficult to motivate the players for that match.
"My players are obviously very disappointed," Solskjaer said. "With the effort they put in against Newcastle, they did not deserve to lose. They are a fantastic bunch who have given everything for the cause, but it was not enough.
"It will not be easy to lift them for the final day. We wanted something to play for in the last game apart from our professional pride to give our supporters a good send off for the summer.
"But this is not the time to reflect on the season. We want to go and do ourselves proud against Chelsea next week."
A win against struggling Newcastle would have been Cardiff's only realistic chance of avoiding the drop but they failed to convert the numerous chances they created and two late home goals sealed their fate.
"It's never nice to be relegated but you just got to show you can bounce back up," the manager added.
"Before this season we have been four seasons at the top of the Championship so it's a club that's very used to challenging at the top, challenging for promotion. So now we've got to use that experience to our advantage.
"Then we have got to use this season as a learning experience of course."
(Writing by Sudipto Ganguly; Editing by John O'Brien)
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