Portsmouth had a scare before overcoming Plymouth Argyle 2-1 in the 'Battle of the Dockyards' FA Cup tie.
Keeper David James made a string of fine saves after Plymouth took a fourth-minute lead through debutant Chris Clark before £5million signing Lassana Diarra equalised with his first goal for the club and then Niko Kranjcar grabbed a 44th-minute winner.
But Argyle, 12th in the Coca-Championship, should have been awarded a penalty 11 minutes from time when Sylvain Distin appeared to handle a left-wing cross in trying to challenge Rory Fallon eight yards from goal.
Referee Andre Marriner awarded only a corner and Sturrock said: "I've seen those given and we had one very much like it a few weeks ago.
"I thought we might also have had a penalty when Lucas Jutkiewicz had his shirt pulled in the last minute but I'm not going to cry about it.
"We have come out with a lot of positives despite a disappointing result. My players were fantastic from start to finish," said Sturrock.
"We could have caved in after Portsmouth's second goal but I made sure we lifted our heads again and gave another great performance in the second half.
"We kept our shape, made more chances and the players did all that was asked of them. Our fans were great, too.
"David James was certainly the busier keeper and I think you'll find he's man of the match in most of tomorrow's papers. In the end just one or two zany moments have cost us dear.
"We made a couple of defensive mistakes that were vital but we are a team in a transitional stage and I'm hoping to bring some more players in before Thursday and this performance shows what we are capable of."
"That was every bit as tough as we thought it would be," he admitted. "David James was outstanding for us and needed to be. Plymouth would have been two up early on but for his saves and we were hanging on a bit at the end.
"But you need a bit of luck in the FA Cup and we've got through. I expect one of the top four in the Premier League will win it in the end as usual but when we've got our strongest side we can give anyone a game.
"We didn't have anybody to break forward and support Benjani Mwaruwari in the second half and we ended up dropping a bit deep and inviting pressure.
"But luckily we've got top quality players like Lassana now and we had enough to get through.
"Sol Campbell was missing again and that didn't help but Plymouth did very well and its a credit to them."