There was also concern it would escalate to affect more products.
Parker said it was worrying but important to show restraint so retaliations did not spiral out of control.
New Zealand exports about $8 billion of goods to the US each year, mainly meat, dairy products, and wine.
Trump's announcement of tariffs has prompted China to consider retaliatory tariffs and the European Union said it would impose tariffs on US goods such as bourbon and Harley Davidson's – to which Trump tweeted that he would return serve by boosting tariffs on European cars.
National leader Simon Bridges said it would leave New Zealand vulnerable if Trump went ahead but he did not believe New Zealand should retaliate.
"When one seriously big player, the world's biggest economy the US, goes this way others follow suit.
There's no question that would have an effect through to Australia and New Zealand. Let's hope it doesn't get to that."
Parker said the US move underlined the importance of the revised Trans Pacific Partnership, which he will travel to Chile to sign this Thursday. That would open access to Japan, the world's third largest economy, as well as nine other countries.
Bridges said the agreement would be good for New Zealand and his party would support it.
However, he questioned why National's trade spokesman Todd McClay was not invited to the signing given most of the agreement was negotiated under the former National government.
"There's no way we are going to be the party that is holding this up given how important it is for New Zealand. But it would have been good if they had included Todd McClay given his role was significant and also the need for bipartisan support."
While others – including businesspeople, exporters and even arch-critic Jane Kelsey – had been invited for the signing, nobody from National was included.
Parker said McClay was in Opposition rather than Government and he did not recall being invited to signings himself when he was Opposition trade spokesman.
"While there may be advantages in taking Opposition representatives during the negotiation phase there is no advantage in adding to the cost to taxpayers at the official signing."
Others invited would have to cover their own costs.
McClay had sometimes taken Opposition MPs on trade trips with him, including taking Winston Peters to Europe in the wake of Brexit.
Labour had initially opposed the agreement, now known as the Comprehensive, Progressive Trans Pacific Partnership, but signed it after some last-minute changes following the withdrawal of the United States.
While NZ First will now support it, the Green Party remains opposed, meaning National's votes are needed for legislation to ratify it.
National faced years of protests over the controversial trade agreement and while the protests have eased since Labour came into office, there is a final week of protests from Whangarei to Dunedin to protest the signing – including at Parliament on Thursday.
