Manchester City improved a lot this year.
Gundogan said City can do better and he threw down the gauntlet to their Champions League rivals.
"If we are able to go to the quarter-finals, that's better than last season".
"We defended well and we were clinical - we had four chances and took them all".
Gundogan scored again after half-time to put City in a commanding position ahead of the return leg at the Etihad on March 7.
Even long-term casualty Benjamin Mendy - who damaged cruciate ligaments in September - is making good progress and is expected to play before the end of the season.
Such a handsome lead allowed Guardiola to give Leroy Sane and David Silva runouts on their returns from injury, with Sterling and De Bruyne afforded a rest. "In these kinds of situations it is about more than going through - if we have a draw at home that won't give us a good feeling".
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The Red Devils slumped to their second Premier League defeat in three games to leave them only two points ahead of third-placed Liverpool FC as the race for Champions League qualification hots up.
But Silva, who scored City's second goal on a freezing night in Switzerland, continues to sound a note of caution.
"For a Champions League game we did ever so well".
"Of course, we will be focused against Basel at the Etihad, but with Arsenal and Chelsea to play (in the Premier League) it's important to be focused there, too. It opened up the top four and they are under a little bit of pressure now".
Centre-backs Vincent Kompany and Nicolas Otamendi were unsettled by Oberlin, although penalty claims against the latter found no sympathy from referee Jonas Eriksson.
"I thought the pitch was a bit hard, it was freezing out there", Kompany said, while Guardiola described the pitch as "dangerous".
Basel coach Raphael Wicky admitted his side were outplayed by a ruthless City side.