Saturday's 3-1 win at Derby was Reading's third in four outings and lifted the relegated Royals to seventh, with 15 points from their first eight matches.
"A team coming down is always looked at, rightly the expectation is to be pushing near the top," said Adkins.
"I'm not sure what the stats are for the club in recent times but this will be up there in the last seven or eight years, and we're in the most successful period in the club's history as well.
"We won't get too high or too low. We just want to stay in the race."