The England international missed the FA Cup clash with Newport County on Sunday after his indiscretion but was back in the starting line-up against Wolves in the Premier League on Thursday night.
The 26-year-old scored the opener in a dramatic 4-3 victory but Cole feels not only the night out in Northern Ireland, but his whole season has been a disappointment.
Rashford was fantastic over the previous campaign scoring 17 league goals, but with just five this season it has been a serious drop-off.
Speaking at a Q&A session at Players House in Dubai, via the Daily Mail, Cole said: ‘‘I’m surprised Marcus has found himself in this position again.
‘We never minded a night out when I was playing and everyone is entitled to a night out but ultimately when you do have a night out you need to turn up for training.
‘You can’t go on a couple of nights out and then call in sick – that’s disrespectful.
‘He has found himself in hot water and Erik ten Hag has dealt with it internally and the situation is now over but he needs to have a look at himself.
‘If I was Marcus, which I’m not, but if it was me personally, I would be bitterly disappointed if I found myself in this situation after such a good season last season.’
Rashford is set to be involved when Manchester United host West Ham in the Premier League on Sunday afternoon.
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