The sacked Manchester United boss had a disruptive relationship with Shaw during their time together at Old Trafford.
The coach said the club had "got a good deal" from Inter Milan for Lukaku and wished him the best, while tipping 17-year-old Mason Greenwood to step up to replace the Belgian worldwide.
Jose Mourinho has said Manchester United "have to win" the Europa League this season, if their campaign is to be considered to a success. Everything goes in order of the way it should be done. "Now I'm in that situation for the first team".
"He has been a little unlucky, as he's not the type of player that can create a goal by himself, he needs service".
"When I looked at the bench yesterday [Saturday] and the players that were not even involved, I believe even their B team could fight for the title". It's about having the right players and the right people in and it's not about suddenly changing when you haven't got the right ones.
"I give my life for the club and that's the most important thing".
Solskjaer continued: "As I said earlier last season as well, it's not about a quick fix, it's a long rebuild".
"But within the team and the club, we're feeling very confident and don't feel that negativity you're talking about".
"It's not just me". Right now I feel like mentally and physically I'm more prepared to do it than in the past, especially physically.
And Solskjaer said: "I feel we are on the right track because we have a better squad a better team and a better foundation this season to improve and take that first step".
"The Premier League is a special competition for me, one that takes so much hard work to win and you just can't take your eyes off the matches every week", Mourinho said in a statement released on Saturday morning.
"For me, they have not had a good transfer window".