The Belgian joined Inter in a 65 million euro ($73 million) move earlier this month after two years at Old Trafford.
Lukaku scored 42 goals for the Red Devils, but just 15 of them came last season as he fell down the pecking order once Ole Gunnar Solskjaer replaced Jose Mourinho.
And former Manchester United captain Gary Neville was among those to criticise Lukaku’s physical condition, claiming he weighed over 100 kilogrammes.
“He (Neville) can talk about my fitness but he should never say anything about my professionalism, that I don’t work hard enough,” Lukaku told the BBC.
“That is something he cannot say. All the coaches I have had say the same thing about me.
“What did Ole Gunnar Solskjaer say when I was on the training ground? What did he say? That I always work hard and always do my best to try and improve myself. Same with Jose Mourinho and (Belgium and former Everton manager) Roberto Martinez. Now (Inter coach) Antonio Conte will say it.
“Last year was just a bad year. It happens in football. You just have to move on. I am not going to sit here and react in a negative way.”
Hopes were high that Lukaku could spearhead a new era for United when he joined from Everton for £75 million ($91 million) in 2017, but he left Manchester having failed to win a trophy.
“For me, the Manchester United experience is one I am grateful for – not a good one because we didn’t win and I wanted to win with the club – but they gave me a chance,” added Lukaku.
“I got to play for one of the biggest clubs in the world, so I will always be respectful to them. At the end, I thought it was better for me to move on and try different things.”
Lukaku was particularly complimentary on the way Solskjaer handled his exit.
“Me and Ole tried to work together but at one point I had to be honest with him. He was also honest with me. We found an agreement. I wanted to go. He understood why I wanted to go.
“It is something I will always be grateful to him for. We had a conversation man to man. I told him how I felt and he understood. He will always get massive respect from me and massive protection.”
Alexis Sanchez followed Lukaku’s path by also leaving United to join Inter on a season-long loan deal this week.
United will still pay a large chunk of the Chilean’s reported £400,000 a week wages so keen were they to cut their losses on a disastrous signing.
Sanchez has scored just five times in 45 appearances since joining from Arsenal in 2018, but Lukaku believes the two can form a potent partnership in Serie A.
“He has had a difficult time at Manchester United. Coming here was the right move, in a good dressing room, where the manager wants winners who can really help the team. He is going to be part of that,” said Lukaku.
“He is going to add a lot of competition to the squad we already have. Now it is up to him to show it. I really believe he is going to do well for us.”
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