Grant believes Parker chose West Ham over the Champions League football and an improved salary on offer at Spurs to advance his career.
He said: "There's a lot of talk about money in football. I think money is important but I don't think it's everything. I don't want players who say: 'They are paying me more there so I will go.' Or: 'They are paying me less so I won't go there.'
"They need to check and see everything, the picture, what is the vision of the club. Parker saw the full picture and he stayed. If you are a top player and you have big money you need to choose what is good for you and sometimes that is not to be in a big club."