The 46-year-old, who won 57 caps for England, was fined £1,000 plus further costs totalling £245, had earlier admitted a charge of common assault and also one of being drunk and disorderly following an incident at the town's railway station last month.
He was originally also charged with a further count of assault involving his ex-wife Cheryl - although that charge was subsequently dropped.
Gascoigne, who began his career with Newcastle before playing for several clubs including Tottenham, Lazio, Rangers Middlesbrough and Everton, has battled alcoholism for several years.
The Gatehead-born star admitted assaulting ticket inspector Jack Sherrington when he tried to assist after noticing he was staggering towards the railway tracks.
The court heard that Gascoigne had been travelling from Newcastle to London after visiting his sick father - who has a heart condition - but had alighted from the train at Stevenage.
Gascoigne's lawyer Gavin Harris said he only consumed a small amount of alcohol due to a "combination of stress caused by worry for his father and acute pain from a hip operation six weeks previously".
Harris said that because Gascoigne had not drunk alcohol for a significant period of time, the effects were stronger than would have otherwise been the case.
In a statement outside court, Harris added: "Mr Gascoigne has asked me to
say a few words on his behalf.
"He wants to publicly apologise for his actions that evening.
"He now wishes to be left alone to carry on with his recovery."