The Foxes will return to England's top flight next season after a 10-year absence following defeats for both Queens Park Rangers and Derby County on Saturday.
Nigel Pearson's men had beaten Sheffield Wednesday on Friday evening but, despite achieving promotion, Morgan says that City are keen to now win the Championship.
"It feels fantastic," Morgan told the Leicester Mercury. "We did our job on Friday night and we still have six games to go so we just want to concentrate on becoming champions now.
"It is definitely the greatest achievement of my career so far to achieve promotion. It is amazing and something I haven't done before. To captain Leicester and do it is even more special."
Leicester resume their bid to win the division by hosting Brighton & Hove Albion on Tuesday.