Jamie Vardy was one of a number of players to miss opportunities to equalise against United as Leicester had the better of the second half, and Puel lamented his side's slow start during which Marcus Rashford scored the only goal of the game.
Solskjaer has won eight of his first nine matches in charge, with United travelling to face Leicester at the King Power Stadium on Sunday.
Solskjaer believes Martial has the "capability" to be a 20-goal-a-season player and called on him and Rashford to begin "sniffing" out "scruffy" opportunities. I said United should go for the best off the pitch football brain in the world and the best head coach in the world they can get.
The 23-year-old spoke after the announcement of his contract extension, saying:"I am loving my time at this club".More news: 'Harry Potter' Star Is Not Happy About Tom Brady's Trump Friendship
Solskjaer welcomed back Anthony Martial into the squad after injury but with the Frenchman only fit enough for a place on the bench, the United caretaker handed Alexis Sanchez a first Premier League start since November 3.
United travel to Leicester this weekend knowing they have a chance of climbing back into the top four if results go their way.
Despite his short-term appointment, Solskjaer said the club are consulting him about players they are planning to sign at the end of the season. He " ll be up there but so will Mauricio Pochettino but the next man we [United] get in has to be the right man.
"I think we've risen to most of the challenges. maybe they will make us move to the next level because I think we've given ourselves a chance now to get into the top four maybe earlier than we thought". To get the backing from them was fantastic. I think by being honest with him it's the best place to be.
Chris Smalling was named on the bench on Tuesday night after recovering from a foot injury so he'll be hoping to feature on Sunday but I think he'll be named among the substitutes once again.