Finn took 6-125 to lead the England bowlers’ fightback, but the losses of Alastair Cook and Jonathan Trott have left the tourists struggling, still 393 runs in arrear.
“The loss of two wickets is slightly disappointing but we have people who can assert themselves on the game,” said Finn.
Nick Compton and Ian Bell remained at the crease at stumps after a late Kiwi onslaught.
“It is important we came back with the two guys who are in at the moment and we really try to assert ourselves on the game again – as New Zealand did in the first day,” added Finn.
“They played diligently, they were watchful and they played very well. We’re going to have to do that.”
“We don’t have to worry about the run rate. We have to set ourselves small targets and get to those. When we come back tomorrow we will be looking to survive and accumulate, and then reassess at lunchtime or whenever that might be.”
Finn also heaped praise on the bowling unit, who took nine wickets on day two following a barren first day.
“The energy levels were good,” he said. “We always make an effort to run through the overs so we feel energetic and are able to create something.”
“Yesterday might have seemed from the sidelines as if there wasn’t as much there – but when you take only one wicket in a day maybe it is easy to think that. I felt we were the same both days and thought we were excellent today.”
“We bowled in a manner that meant they couldn’t accelerate as much they may have liked to. When you bat for such a long period you may want more runs on the board but it shows the way we bowled was really good.”