Gareth Bale’s first-half goal was enough to give Wales victory in Cardiff and lift them to the top of Group B ahead of Belgium.
They are now five points clear of Israel in third, with four games to play, two of which are at home.
“It’s a huge step forwards,” Coleman told Sky Sports. “But we have been here before, it doesn’t mean we are going to qualify.
“We asked the players before the game to give everything, we said ‘you can’t hold anything back, we need everything,’ and we got that.
“It wasn’t one of our best performances, it was a bit scrappy, but we just dug in, that’s what we do when we are not playing well, we don’t lose easily and we sacrificed a bit of imagination and dug in as a team.”
The result continues an impressive qualifying campaign for Wales, who were ranked 112th in the world only three years ago.
They have taken 14 points from their six matches and Coleman paid tribute to the fans at the Cardiff City Stadium.
“We have been fighting a long time for an atmosphere like this and I have never witnessed one like it,” he said.
“I thought our supporters were unbelievable, when we sang the national anthem at the start it was incredible.”
Coleman’s also praised his side’s braveness, saying: “We needed brave men tonight…even if we had come off without the points we said all along we wanted to get our supporters back onside, to be proud of our team, and they will be proud if they see committed players like tonight.”