Solskjaer, while satisfied after his first six months in charge, is demanding the board bankroll a major buying spree this summer.
The former Manchester United manager said: "The verdict on our fourth place has not actually been decided today. The results achieved throughout the season have brought us to this point.
"When we started our tenure, we were in sixth or seventh place. We tried to take the team higher and we succeeded. However, in the games we should have dominated, we failed to do so. Next season we will try to do that."
On the summer transfer market, Solskjaer also said: "I can't say exactly what roles we will buy players for, but we will get someone for defense, midfield and attack. We need them.
"We need to buy players who can bring quality both in training and in matches. We are having meetings, we are talking. We need to bring the right players. We don't have the luxury of making mistakes. We need to get good, ambitious players so that they can help the team grow."