Aaron Doran opened the scoring for the Highlanders but the League Cup finalists needed a 74th-minute headed goal from Billy Mckay to secure a fifth-round replay.
Hughes bemoaned his side failing to build on their 40th-minute lead but he added: "I loved every single minute of the match. Credit to Stranraer, they just about managed to pull it off.
"But once again we don't do anything easy at Inverness. We showed character to come back from it and dug deep to equalise.
"Apart from one of two breakaways I thought we hemmed them in and we might have scored one or two goals. That might have been a bit hard on Stranraer though. They deserve their replay."
Despite having no complaints about the penalty award, for Graeme Shinnie's foul on Martin Grehan, the Caley Thistle manager was not happy with the way his side conceded.
"We gave them two goals," he said. "The penalty and the breakaway. They were really clinical with their finishing. There's a bit of me saying: 'Really well done, Stranraer'. The tie is not over."
Stranraer manager Stevie Aitken thought his side would have earned a place in the next round if they had held on to their lead slightly longer.
Grehan netted from the spot-kick on the stroke of half-time and Jamie Longworth struck his 20th goal of the season with an emphatic finish but the Scottish Premiership side were level two minutes later when McKay converted Richie Foran's cross.
Aitken said: "I thought we gave a great account of ourselves against a really good side. To match them over 90 minutes was pleasing.
"I thought that if we held on another 10 minutes without losing a goal then we might have been able to get to the finishing line.
"I can't complain too much but to lose it the way we did was frustrating, I thought we gave them a soft goal."