The Mayor stressed that everyone "desperately needs this lockdown to be the last" and asked for common sense to be applied alongside sticking to the current regulations.
Lockdown rules were eased at the start of this week to allow "rule of six" gatherings or meetings of two households outdoors while amateur sport is also now acceptable.
Households are also no longer explicitly told to "stay local" but instead to minimise travel.
However, Mr Preston urged that small compromises such as wearing a mask and maintaining social distancing continue strictly to build on the progress made in recent weeks and months.
He said: "We've made so much progress thanks to the rollout of the vaccine programme and the fact the vast majority of people are doing the right thing.
"We've made so much effort to get to the point we're at now and it's crucial we don't undo that.
"The only people not following the rules now are disrespecting everyone else in the town.
"We all must keep on making the small compromises such as wearing a mask in public places to keep the virus at bay.
"We desperately need this lockdown to be the last and for that reason it's crucial people use their common sense and celebrate Easter within the rules."
- For the latest local updates and information, visitmiddlesbrough.gov.uk/covid19
For information on local help and support, visit www.middlesbrough.gov.uk/helpboro
For advice for clinically extremely vulnerable residents call Middlesbrough Council's support line on 01642 729777
The latest advice from Government and Public Health England can be found at https://www.gov.uk/coronavirus