Adam enjoying Stoke momentum
Hughes - who was appointed Potters boss in May - oversaw a 1-0 loss at Liverpool on the opening day of the Barclays Premier League season in his first competitive match in charge, and at half-time in his second match on Saturday the Staffordshire outfit were trailing 1-0 at home to newly promoted Crystal Palace.
They bounced back in the second half of that league fixture, however, as goals from Adam and Ryan Shawcross four minutes apart steered them to a 2-1 win.
And four days later, they had their second victory under Hughes as Sky Bet League One side Walsall were beaten 3-1 at the Britannia Stadium in the second round of the Capital One Cup, with Kenwyne Jones bagging a hat-trick.
Suddenly, ahead of Saturday's league trip to West Ham, Hughes' Stoke tenure appears to be properly up and running - which is why Adam, despite being proud to play for Scotland, is a little disappointed his focus will have to be away from the Potters after the Upton Park clash.
Asked after Wednesday's Walsall game if he was looking forward to the international break, Adam, who is set to feature for his country in World Cup qualifiers against Belgium and Macedonia on September 6 and 10 respectively, said: "No, not really - I want to keep playing (for Stoke).
"This is a big season for us and we want to keep playing.
"The international games are great as well when you go and represent your country.
"But from a club point of view, if we can go and win on Saturday, that will be six points and it will give us confidence for a tough home game against Manchester City when we come back."
Stoke, with a starting XI showing eight changes from the Palace match, took the lead against Walsall in the 22nd minute when Jones collected the ball following an error by Saddlers midfielder Sam Mantom and rifled it into the net.
Nine minutes later, the Potters striker scored again, firing home when the ball dropped at his feet from a corner and, after Ashley Hemmings had been allowed the space to pull a goal back for the visitors in the 57th minute, Jones completed his treble six minutes from time, coolly finishing having raced on to a through-ball.
Stoke play another League One side, Tranmere, away in the third round and Adam said: "We tried to apply ourselves in the right way and in the end we won the game.
"It was important that we got it done in 90 minutes with no hiccups really.
"We lost a goal which we are disappointed in, but at the start of the game we would have taken 3-1 and we'll look forward to Tranmere when it comes around."
Walsall boss Dean Smith was encouraged by his players' efforts.
"We try to create an environment for players to go and play and express themselves," Smith said.
"It was a good stage for them to go and do that.
"I said to them before the game 'everyone says go and enjoy it, but I don't want you to enjoy it - I want you to do the right things and play well'.
"They certainly did that."