The Blues also received sympathetic noises from the EFL’s head of referring Mike Jones, according to Cowley, which also prompted a re-examination of the decision taken by referee Sam Barrott at the time.
Morrell faces an automatic three-match ban if the Blues’ appeal is turned down.
A Football Association decision is expected today – hours before Pompey face Burton at Fratton Park.
The FA have already acted decisively today with the decision to overturn Bolton captain Ricardo Santos’ dismissal for hand ball during the Trotters’ 1-1 draw with Morecambe on Saturday.
The defender is now available to face Charlton tonight in League One.
And Cowley expects a similar outcome before his side’s game against the Brewers, having made contract with the governing body before yesterday’s deadlne.
Speaking to The News, the Blues boss said: ‘We spent Sunday trying to find the best footage and unfortunately the footage from the side angle is not clear.
‘It is probably the same view the referee had, which was an impeded one.
‘Ultimately, Louis Thompson and Cameron Brannagan are right in the way of the challenge and I don’t understand how the referee comes to the decision because he can’t see it and that’s clear.
‘We, thankfully, yesterday morning managed to find footage from the Go-Pro in the Oxford United net and that gives us a much clearer indication of the challenge.
‘Like we felt, Joe is five foot five so he’s only got little legs and they don’t get up high anyway.
‘The ball was high so the foot was high, he nicks the ball before Cameron Brannagan can get there and there is no contact.
‘We think we’ve got really good grounds for appeal.
‘We spoke to Mike Jones, the head of refereeing at this level, and his exact words to me were that it was a very, very harsh sending off.
‘We’ll have to wait and see what the panel says, but we believe we've got grounds to appeal and I anticipate Joe being available (against Burton).’