Back-to-back home Premier League wins over Newcastle United and Johnson's former club Manchester City since Gus Poyet took charge have lifted Sunderland off the foot of the table.
Next up is a trip to the Britannia Stadium to face a Stoke side three points above Poyet's men in the table, before Sunderland head to Villa Park the following weekend.
Stoke and Villa have each lost five out of 11 league games this season, fuelling Johnson's belief that Sunderland can continue their recent revival against the duo.
"We've got a couple of good games coming up now," he told the Sunderland Echo.
"The home games haven’t been kind in recent weeks, but now we've got some winnable away games.
"If we can keep a clean sheet, we know we can cause problems with our attack.
"I think it's important to go to Stoke and carry on what we've been doing and then we should come out with a good result."
On Sunderland's upturn in fortunes under Poyet, the winger added: "Now we're back in touching distance.
"If we can get another three or four points over the next few games, people won't be writing us off again.
"There's so much more football to be played. We didn't get carried away by where we were at the beginning of the season.
"We're still in a bit of trouble, but it looks a lot better now.
"The two home wins (against Newcastle and Southampton in the League Cup) before Man City lifted us massively anyway. But that win gave us an extra lift going into the international break. That win was huge for us."
