Middlesbrough have now gone seven consecutive seasons since they last won an opening day fixture.
"For a long period thought we were on course to win it," claimed Southgate.
"After the McCarthy injury there was a long stoppage and we seemed to lose a bit of momentum.
"They scored two top-quality finishes but we still kept coming back and when the chance in the last minute did not go in you just think this is not going to be our day.
"I'm not down though because we showed a lot of promise against a good and experienced side but it is a bit like air being let out of a balloon - we are deflated."