Following Scotland's defeats to Georgia and Germany, the Boys in Green have strengthened their position in third, opening up a gap of four points to Gordon Strachan's side in Group D, while just two points separate Ireland from second-place Poland.
With crucial ties to come against Germany and Poland in October, the Donegal native now has his sights set on winning the next game.
"We're going to win our next game and win the game after that, that's what we're looking at," Coleman told reporters. "All I want to do is win the next game and go from there.
"It has been a great week. How tight the group is, it just turned around in our favour," added the 26-year-old. "Scotland didnt have the best week and we had a great week and we're delighted with the turn of fortune.
"There's a great buzz [in the dressing room]. There was a great buzz on Friday night too [after the Gibraltar win]. We're happy with how the week went.
"We wanted six points this week and we go into the next games [against Poland and Germany] fully focused, fully concentrate. We've done nothing yet."
Meanwhile, the Blues full-back was fulsome in his praise of Jonathan Walters, who scored the decisive goal on the 69th minute after meeting a Jeff Hendrick cross.
"Jonny [Walters] is different class," Coleman declared. "He's someone you'd want in your team every week.
"You can see the attitude he has and we're happy to have him."
Ireland continue their quest for Euro 2016 qualification in October when they host Germany before playing Poland away.