Solskjaer has been in charge for almost two years though is yet to win a trophy during his tenure at Old Trafford.
Asked what the aims are for the season by MUTV, the manager said: “The boring answer is we have to keep on developing!
“We have to keep on improving and have that culture going forward of trying to improve every single day. I think we've earned the right to go into this season feeling positive and with confidence.
“The way we finished the season was strong but also we finished it with a bit of a bitter taste because of the last game we lost to Sevilla in the semis – a game that we played really well in and could have won.
“So we're getting closer and closer to challenging and winning trophies and we need to take it another step forward.
“I know there are loads of other clubs really looking to improve and everyone always wants to do that every season. We need to be better than last year.
“We're a year older too. Everyone is, but we were the youngest squad in the Premier League last season and the year's experience that these boys have had now will stand us in good stead, I'm very sure of that.
“We'll have to start the season better than we did last season. That's the aim now: that we get a good start and, from then on, kick on."