The Saints claimed a 4-3 victory over local rivals Morton at Cappielow in a second-round derby cracker and McGowan is desperate to stay in Paisley in the next round.
With Morton having led 2-1 at the break, it seemed that Buddies' 12-year domination of their Renfrew rivals in competitive encounters was in danger, but the diminutive attacker saluted the character shown by his side to come from behind.
Now the former Celt is desperate to go as far in the tournament as possible and is confident Saints can get the better of all-comers at Greenhill Road.
McGowan said: "We are hoping for a home tie now. The golden rule of cup football is to make the next round and we did that.
"It was never going to be easy coming to Cappielow for a derby and Morton made it tough. When we went in 2-1 down we knew we would have to dig deep."
He added: "But we have done that and the support from the St Mirren fans was awesome – and for them, as much as the lads, we are looking for a home tie. We believe in Paisley we can give anyone a game."
McGowan has no doubt that the Cappielow cracker gave the fans value for money and also underlined the mental toughness within the Paisley ranks.
He added: "It was a great game for the punters. We felt we weren't at our best, but the boys had to show great character.
"We are committed to playing football the way it should be but I think we showed we can dig deep when needed.
"Credit to Morton, they had a real go and after we had missed the two great chances at 4-2 up and they pulled one back it was a bit nervy. So it is a great tie to have behind us and now we will just wait and see what the draw hands us."
As usual, Saints' commitment to playing the passing game was evident early on.
With eight minutes gone, Jim Goodwin's powerful 20-yard drive was adjudged by referee Calum Murray to have been handled by Grant Evans deliberately. From the resulting free-kick, Gary Teale opened his Saints account with a superb rising strike which beat Colin Stewart.
But Allan Moore's men bounced back when Michael Tidser and Peter MacDonald enjoyed a neat exchange of passes that allowed the former to run through and slot home.
Ex-Celt Tidser then turned provider to play in MacDonald and the former St Johnstone striker curled in a fine finish.
Saints gaffer Danny Lennon moved to a midfield five after the break and his side soon reclaimed control. Nigel Hasselbaink surged clear before picking out Stevie Thompson, who slotted home from six yards.
Former PSV kid Hasselbaink was then adjudged to have been chopped in the box by Ton skipper Stuart McCaffrey, with the Dutchman sending Colin Stewart the wrong way from the spot.
Saints made it 4-2 when Jeroen Tesselaar's superb cross found Thompson, who bulleted in a header. But Ton sub Andy Jackson replied to ensure a nervous finish for Saints on a night that will live long in the memory.