Wales manager Gary Speed said his young side showed great maturity in securing
Gareth Bale's deflected shot proved enough to secure a third win in four Euro 2012 qualifiers as Wales finished fourth in Group G.
"We have come so far in such a short space of time - that's why I thought this game might have been a banana skin for us," said Speed.
"It might have been a bridge too far but the players were fantastic."
The victory in an almost deserted Vasil Levski stadium gave Wales their first back-to-back wins in competitive matches for six years.
Friday's 2-0 win over Switzerland in Swansea had lifted Speed's side off the bottom of the group at the expense of Bulgaria, who were playing their first competitive game since sacking manager Lothar Matthaus.
"I was pretty apprehensive before the game," revealed Speed, who took over with Wales bottom of the group with no points from three games.
"I would have taken 0-0 before the game because it's a difficult place to come. And obviously after our win on Friday it was a situation the players haven't found themselves in very often.
"We've come here probably as favourites and with all the furore surrounding the Bulgaria team, I felt a slip-up was on the cards.
"But the players proved me wrong and they took to their task really well and dug out a great result."
Bale again proved to be Wales' most potent attacking threat, and his marauding runs down the right flank paid off just before the break as his low short wrong-footed Bulgaria goalkeeper Nikolay Mihailov after flicking off Ivan Ivanov's heel.
The 22-year-old Tottenham Hotspur midfielder then almost added a double but his beautifully struck volley crashed against in inside of the bar in the second half.
"We hadn't won two successive competitive games in six years so it was nice to get that off our backs," said Bale, who took his goals tally to five in 32 appearances.
"To get the victory was vitally important. We knew it was going to be a very difficult task coming here.
"We trained on the pitch the night before and the surface was dreadful to be honest. So it was a great victory and one we worked hard for."
Bale believes Wales can now start to plan with renewed belief for the 2014 World Cup qualifiers, which start in September 2013.
"The most important thing for us is that we're improving with every game," he added.
"As long as we continue to do that and head in the right direction then I'm sure we can achieve what we want."