The Shrimpers had to settle for a share of the spoils after Pools midfielder Bradley Walker's volley cancelled out Barry Corr's opener.
"We had what I thought was a stonewall penalty turned down in the first half and also missed a one-on-one so we had the chances to win it," said Cooper.
"However, once we went behind it was always going to be difficult and I was proud by how the players galvanised themselves to get something from the game.
"The younger lads would have learned plenty from that match and credit to those for have been around the block a bit because they certainly played a part.
"But it was a good game of football as both teams tried to play the game the right way and a draw here is a good result for us."
Southend, who have now not won in eight games, came close to taking the lead when recalled winger Anthony Straker headed a right-wing cross from John White against the crossbar.
They took the lead in the 43rd minute when Corr impressively converted a low left-wing cross from Kevan Hurst with a near flick.
Straker had a well-struck shot well saved by Hartlepool goalkeeper Scott Flinders at the start of the second half before Hartlepool equalised when Walker collected a loose clearance from Michael Timlin and volleyed home from 20 yards.
Southend pushed hard after being pegged back and almost went back in right when Hurst had a shot blocked on the line by full-back Darren Holden.
But Hartlepool also came close to going back in front when Luke James saw his shot tipped wide of the post by Daniel Bentley.